bluuebunny/crossref_metadata_2025 huggingface dataset:
PENYULUHAN PRINSIP-PRINSIP GOOD MANUFACTURING PRACTICES (GMP) PADA HOME INDUSTRY OLAHAN SINGKONG DAN UBI DI DESA TOKELAN, KECAMATAN PANJI, KABUPATEN SITUBONDO
Authors: Yekti Gema IA , Suryaningsih Yasmini
Published: January 2020

Desa Tokelan merupakan salah satu desa yang ada di Kecamatan Panji yang memiliki beberapa home industry yang masih tradisional. Beberapa home industry yang masih tradisional yaitu home industry keripik singkong Jaya dan home industry Karang Mas Mbak Nur. Keduanya masih belum menerapkan prinsip-prinsip GMP dalam usahanya. Lingkungan produksi dari keduanya juga masih cenderung sederhana dengan memanfaatkan pekarangan rumah sebagai tempat produksi. Tata letak proses produksi pun tidak sesuai dengan prinsip GMP. Hal tersebut terjadi karena keterbatasan pengetahuan dan keterampilan mereka tentang prinsip GMP. Oleh sebab itu, penyuluhan tentang penerapan prinsip GMP perlu dilakukan untuk meningkatkan kualitas dan keamanan produk. Selain itu, prinsip GMP juga dapat menjamin kesehatan dan keselamatan pekerja. Penyuluhan penerapan prinsip GMP dilakukan dengan metode ceramah, diskusi, dan pendampingan. Materi yang akan disampaikan meliputi konsep keamanan pangan, bahaya-bahaya yang terkait produksi pangan olahan, prinsip-prinsip GMP, serta penerapan prinsip GMP.

Kata kunci: keamanan pangan, GMP, prinsip-prinsip GMP
PEMBUATAN MINUMAN HERBAL INSTAN DI KELURAHAN BANYUMANIK KOTA SEMARANG
Authors: Muflihati Iffah , Affandi Arief Rakhman
Published: January 2020

Kelurahan Banyumanik khususnya RW IV dan RW V memiliki anggota PKK yang potensial untuk diberdayakan secara ekonomi melalui pengolahan bahan makanan. Permasalahan yang dihadapai adalah ketersediaan tanaman herbal di pekarangan yang belum termanfaatkan. Para ibu rumah tangga memiliki keinginan untuk menghasilkan produk olahan dari tanaman herbal yang memiliki kemudahan dalam penanganan dan memiliki umur simpan yang lama. Kegiatan pengabdian IbM ini bertujuan untuk memberdayakan para ibu rumah tangga di RW IV dan RW V Kelurahan Banyumanik Kecamatan Banyumanik Kota Semarang melalui pengolahan minuman herbal instan. Luaran yang akan dihasilkan dari pengabdian ini antara lain dokumen keanggotaan PKK, produk olahan minuman instan dari tanaman herbal yang telah diketahui kandungan gizinya, merk dagang, dan nomor PIRT yang beredar di minimarket dan toko oleh-oleh. Kegiatan ini dilakukan melalui tahapan sosialisasi, pelatihan pengolahan tanaman herbal menjadi minuman instan, analisis kandungan zat gizi, perizinan PIRT, dan evaluasi. Hasil yang didapatkan yaitu peserta pengabdian memiliki kemampuan mengolah tanaman herbal (jahe, kencur dan kunyit) menjadi produk minuman instan (jahe instan, beras kencur instan, dan kunyit asam instan).
PKM PELATIHAN PEMBUATAN PRODUK CINDERAMATA ACRILIC BERBAHAN DASAR LIMBAH KAYU GMELINA DAN PEMASARAN ONLINE PADA KELOMPOK USAHA BERSAMA (KUB) SEKAR PUTIH SITUBONDO
Authors: Hamdun Edy Kusnadi
Published: January 2020

Produk cindera mata acrilic memiliki nilai ekonomi yang tinggi, dimana harga kisaran yang ditawarkan di pasar mencapai ratusan ribu rupiah. Banyaknya limbah meuble di wilayah Situbondo, utamanya kayu gmelina cukup menjadi peluang untuk bisa dijadikan produk-produk kerajinan seperti cinderamata. Mitra yang terlibat dalam kegiatan ini adalah Kelompok Usaha Bersama (KUB) “Sekar Putih”, Kelompok usaha ini merupakan perkumpulan masyarakat yang akan memulai wirausaha pengolahan limbah kayu gmelina menjadi produk cinderamata acrilic. Kegiatan ini memberikan pembinaan bagi KUB “Sekar Putih” untuk berkembang cepat hingga mampu menciptakan produk yang inovatif dan pola pasar baru sehingga mampu menghadapi persaingan di era digital. Hasil luaran dari kegiatan ini berupa jasa, model, metode, system, produk/barang, dan paten. Luaran lain yang ingin dicapai adalah menumbuhkan wirausaha yang maju dan berinovatif, meningkatkan pengetahuan tentang pemanfaatan limbah kayu, menciptakan produk cinderamata acrilic yang unik dan modern, meningkatkan pengetahuan pemasaran online dengan media e-commerce dan sosial media sehingga meningkatkan pangsa pasar produknya, dan meningkatkan pendapatan dan kesejahteraan keluarga anggota KUB “Sekar Putih”.
DIVERSIFIKASI ALGA ULVA MENJADI KRIPIK DAN KRUPUK NORI DI DESA DUWET KECAMATAN PANARUKAN KABUPATEN SITUBONDO
Authors: Listriyana Ani , Pahlewi Anita Diah
Published: January 2020

Pantai pathek Selatan Desa Duwet menyimpan potensi laut yang sangat besar yang belum dikelola dengan baik yaitu alga Ulva. Selama ini masyarakat Desa Duwet menjualnya dengan harga Rp. 1.300 untuk berat ulva kering. Oleh karena itu kami memberikan pelatihan kepada masyarakat Desa Duwet tentang pengolahan alga menjadi stik dan kerupuk nori dengan harapan setelah mendapatkan pelatihan, akan mereka lanjutkan untuk usaha. Sebelum pelatihan , kami melakukan uji organoleptik kepada beberapa orang terkait produk yang akan kami berikan penyuluhannya kepada masyarakat. Hasilnya mereka menyukai produk stik dengan jumlah nori yang lebih banyak. Pasca pelatihan yang dihadiri kurang lebih 20 ibu-ibu ini yang pada akhirnya mereka membuat kelompok “ulva Lestari” sepakat untuk melanjutkan usaha stik nori dibandingkan kerupuk Nori karena pembuatan stik membutuhkan waktu yang lebih sedikit dibandingkan dengan kerupuk. Sampai saat ini sudah beberapa kali pemesanan stik nori melalui ibu-ibu yang telah mengikuti pelatihan ini. Pendampingan akan terus dilakukan hingga mereka bisa mandiri dan mempunyai pasar yang cukup luas.
TRANSFORMASI CEPAT SAMPAH RUMAH TANGGA MENJADI PUPUK ORGANIK MELALUI “TAKAKURA” SEBAGAI UPAYA OPTIMALISASI SAMPAH ORGANIK RUMAH TANGGA
Authors: Dewi Yuni Kartika , Siswoyo Nurul A. Silvi
Published: January 2020

Dewasa ini sampah selalu menjadi permasalahan bagi lingkungan. Sebagai wujud kepedulian terhadap penanganan sampah maka perlu dilakukan tindakan pengelolaan sampah dimulai dari skala terkecil yaitu dalam rumah tangga. Kemajuan ilmu dan teknologi menimbulkan dampak positif bagi perkembangan perekonomian masyarakat karena banyak produk-produk yang dihasilkan akibat proses teknologi yang ada, salah satu produknya adalah kompos yang dihasilkan melalui metode “Takakura”. Tujuan dari pengabdian masyarakat ini adalah untuk turut serta peduli mengurangi jumlah sampah di kalangan rumah tangga dengan cara optimalisasi sampah organik menjadi lebih bernilai guna dan nilai jual melalui aplikasi teknologi tepat guna “Takakura” sebagai salah satu sarana membuat pupuk organik yang cepat dan mudah serta dapat dilakukan di lahan sempit. Penyuluhan dan pelatihan pendampingan pembuatan kompos dilaksanakan di Desa Panji Lor Kebupaten Situbondo bersama Ibu-ibu PKK Desa Panji Lor. Kegiatan ini dilakukan dengan metode demontrasi dan praktik pendampingan selama satu bulan. Pelaksanan kegiatan ini berjalan lancar, antusias dan menghasilkan produk olahan sampah berupa kompos melalui aplikasi metode tepat guna “Takakura”.
МОДЕЛЮВАННЯ РОБОТИ КОТКА ДЛЯ ПОДРІБНЕННЯ РОСЛИНННИХ РЕШТОК ТА ОБГРУНТУВАННЯ ЙОГО ПАРАМЕТРІВ
Authors: Голота Б.М. , Кірчук Р.В. , Тарасюк В.В.
Published: January 2020

У статті наведено огляд конструкцій та виконано аналіз процесу подрібнення рослинних решток в полі задля збільшення вмісту органіки у ґрунті. Представлено модель роботи котка та запропоновано методику встановлення його параметрів.
ПИТОМА ВАНТАЖОПІДЙОМНІСТЬ І МАСА ТРАКТОРНИХ ПРИЧЕПІВ ЯК ЗАСОБІВ ТРАНСПОРТУВАННЯ ЛЬОНОТРЕСТИ
Authors: Лімонт A.C. , Лімонт З.А.
Published: January 2020

Досліджені розподіли номінальної і питомої вантажопідйомності тракторних причепів. Вивчена і проаналізована маса цих транспортних засобів. Висвітлено статистичний зв’язок питомої вантажопідйомності і маси тракторних причепів.
ДОСЛІДЖЕННЯ РОЗМІРУ КОМІРЧИНИ ГРАНУЛЮЮЧОГО ТРАНСПОРТЕРА
Authors: Цизь І.Є. , Квач І.В. , Цьось В.В. , Хвесик В.В. , Лавренчук В.В.
Published: January 2020

У статті наведена теоретичне обґрунтування до встановлення залежності розміру комірчини гранулюючого транспортера. Визначений раціональний склад та вологість органо-мінеральної суміші на основі сапропелю.
Visitor profiling using characteristics of socio-demographic and spatial behavior as tools to support the management of protected mountain areas
Authors: Švajda Juraj , Masný Matej , Koróny Samuel , Mezei Adalbert , Machar Ivo , Taczanowska Karolina
Published: January 2020

Protected mountain areas are attractive tourist destinations, and the number of visitors to these areas is increasing. The extension of cable car operations into the summer season is a challenge for some protected areas. Our study focuses on visitor profiles and is based on the characteristics of socio-demographic and spatial behavior of cable car users of the Chopok area (Slovakia). The methods used involve recording visitors’ itineraries through the use of GPS loggers and conducting post-trip interviews with the study participants. In order to better understand visitors’ spatial behavior, the relationship between socio-demographic characteristics and trip itinerary parameters was analyzed. Additionally, three distinct visitor profiles based on cluster analysis were found in the investigated sample. The results can be used to enrich our knowledge concerning the spatial behavior of tourists in mountain environments, and more directly, for the management of cable car destinations located within protected areas.
The Indian Geopolitical Thought
Authors: Križan Ľuboš , Baar Vladimír
Published: January 2020

Since its independence in 1948, India has strived to become a major geopolitical power in South Asia, and an important player in the world. Early on, India achieved significant successes especially in the developing world. Failures caused by the lost war with China include, the rise of separatism and international isolation. After 1990, India gradually became an undisputed leader in South Asia but has since faced a number of important challenges. India is trying to consolidate its geopolitical position. The main goal of the article is to analyze Indian geopolitical thought, its sources, and relevance in Indian geopolitics.
Analysis of Character Education Strengthening Program Management In SMP Muhammadiyah 3 Depok
Authors: Basyir Azhar
Published: January 2020

This studies describe the management of character education strengthening program (PPK) at SMP Muhammadiyah 3 Depok. The types of this research is descriptive-qualitative. the techniques of data collections using observation, interviews, and documentation. The results of this study are (1) The activities of PPK include flag ceremonies, 7S (senyum-smile, salam-peace in greetings, sapa-greetings, sopan-respectful, santun-courtesy, sigap-enthusiasm),  (2) The management of the PPK program runs with a good formulation and has clear purpose. (3) Supporting factors for this program are adequate facilities and infrastructures, the presence of adequate and militant young teaching staff, principals who are classified as young and have a good work ethic.
Evaluasi Pembelajaran Pendidikan Agama Islam (Studi di SMK Muhammadiyah 1 dan SMK Muhammadiyah 2 Kota Palembang)
Authors: Azizah Nur , Zainudin Muhammad
Published: January 2020

The research objective was to determine the evaluation of PAI Learning in SMK Muhammadiyah 1 and 2 Palembang city and technical evaluation conducted at SMK Muhammadiyah 1 and 2. This type of research is a qualitative descriptive study, data collection techniques using observation techniques, interviews, and documentation. Data analysis techniques use the framework of inductive and deductive thinking. The results of the study, the implementation of the evaluation is taken from the results of daily tests, midterm and final exam, the management of the evaluation includes planning, managing the implementation of the organization and evaluation. Technical Evaluation of PAI Learning leads to the cognitive domain, affective domain and psychomotor domain. PAI Learning Evaluation techniques implemented in SMK Muhammadiyah 1 and 2 are test and non-test techniques.
Balanced Online Ramsey Games in Random Graphs
Authors: Prakash Anupam , Spöhel Reto , Thomas Henning
Published: January 2020

Consider the following one-player game. Starting with the empty graph on $n$ vertices, in every step $r$ new edges are drawn uniformly at random and inserted into the current graph. These edges have to be colored immediately with $r$ available colors, subject to the restriction that each color is used for exactly one of these edges. The player's goal is to avoid creating a monochromatic copy of some fixed graph $F$ for as long as possible. We prove explicit threshold functions for the duration of this game for an arbitrary number of colors $r$ and a large class of graphs $F$. This extends earlier work for the case $r=2$ by Marciniszyn, Mitsche, and Stojaković. We also prove a similar threshold result for the vertex-coloring analogue of this game.
The Lower Tail of the Random Minimum Spanning Tree
Authors: Flaxman Abraham D.
Published: January 2020

Consider a complete graph $K_n$ where the edges have costs given by independent random variables, each distributed uniformly between 0 and 1. The cost of the minimum spanning tree in this graph is a random variable which has been the subject of much study. This note considers the large deviation probability of this random variable. Previous work has shown that the log-probability of deviation by $\varepsilon$ is $-\Omega(n)$, and that for the log-probability of $Z$ exceeding $\zeta(3)$ this bound is correct; $\log {\rm Pr}[Z \geq \zeta(3) + \varepsilon] = -\Theta(n)$. The purpose of this note is to provide a simple proof that the scaling of the lower tail is also linear, $\log {\rm Pr}[Z \leq \zeta(3) - \varepsilon] = -\Theta(n)$.
A Short Proof of a Theorem of Kano and Yu on Factors in Regular Graphs
Authors: Volkmann Lutz
Published: January 2020

In this note we present a short proof of the following result, which is a slight extension of a nice 2005 theorem by Kano and Yu. Let $e$ be an edge of an $r$-regular graph $G$. If $G$ has a 1-factor containing $e$ and a 1-factor avoiding $e$, then $G$ has a $k$-factor containing $e$ and a $k$-factor avoiding $e$ for every $k\in\{1,2,\ldots,r-1\}$.
Compositions of Graphs Revisited
Authors: Huq Aminul
Published: January 2020

The idea of graph compositions, which was introduced by A. Knopfmacher and M. E. Mays, generalizes both ordinary compositions of positive integers and partitions of finite sets. In their original paper they developed formulas, generating functions, and recurrence relations for composition counting functions for several families of graphs. Here we show that some of the results involving compositions of bipartite graphs can be derived more easily using exponential generating functions.
A Note on The Rogers-Fine Identity
Authors: Fang Jian-Ping
Published: January 2020

In this paper, we derive an interesting identity from the Rogers-Fine identity by applying the $q$-exponential operator method.
The Borodin-Kostochka Conjecture for Graphs Containing a Doubly Critical Edge
Authors: Rabern Landon
Published: January 2020

We prove that if $G$ is a graph containing a doubly-critical edge and satisfying $\chi \geq \Delta \geq 6$, then $G$ contains a $K_{\Delta}$.
A Note on a Problem of Hilliker and Straus
Authors: Jańczak Mirosława
Published: January 2020

For a prime $p$ and a vector $\bar\alpha=(\alpha_1,\dots,\alpha_k)\in {\Bbb Z}_p^k$ let $f\left(\bar\alpha,p\right)$ be the largest $n$ such that in each set $A\subseteq{\Bbb Z}_{p}$ of $n$ elements one can find $x$ which has a unique representation in the form $x=\alpha_{1}a_1+\dots +\alpha_{k}a_k, a_i\in A$. Hilliker and Straus bounded $f\left(\bar\alpha,p\right)$ from below by an expression which contained the $L_1$-norm of $\bar\alpha$ and asked if there exists a positive constant $c\left(k\right)$ so that $f\left(\bar\alpha,p\right)>c\left(k\right)\log p$. In this note we answer their question in the affirmative and show that, for large $k$, one can take $c(k)=O(1/k\log (2k)) $. We also give a lower bound for the size of a set $A\subseteq {\Bbb Z}_{p}$ such that every element of $A+A$ has at least $K$ representations in the form $a+a'$, $a, a'\in A$.
Combinatorics of Partial Derivatives
Authors: Hardy Michael
Published: January 2020

The natural forms of the Leibniz rule for the $k$th derivative of a product and of Faà di Bruno's formula for the $k$th derivative of a composition involve the differential operator $\partial^k/\partial x_1 \cdots \partial x_k$ rather than $d^k/dx^k$, with no assumptions about whether the variables $x_1,\dots,x_k$ are all distinct, or all identical, or partitioned into several distinguishable classes of indistinguishable variables. Coefficients appearing in forms of these identities in which some variables are indistinguishable are just multiplicities of indistinguishable terms (in particular, if all variables are distinct then all coefficients are 1). The computation of the multiplicities in this generalization of Faà di Bruno's formula is a combinatorial enumeration problem that, although completely elementary, seems to have been neglected. We apply the results to cumulants of probability distributions.
Discrepancy of Sums of Three Arithmetic Progressions
Authors: Přívětivý Aleš
Published: January 2020

The set system of all arithmetic progressions on $[n]$ is known to have a discrepancy of order $n^{1/4}$. We investigate the discrepancy for the set system ${\cal S}_n^3$ formed by all sums of three arithmetic progressions on $[n]$ and show that the discrepancy of ${\cal S}_n^3$ is bounded below by $\Omega(n^{1/2})$. Thus ${\cal S}_n^3$ is one of the few explicit examples of systems with polynomially many sets and a discrepancy this high.
Adding Layers to Bumped-Body Polyforms with Minimum Perimeter Preserves Minimum Perimeter
Authors: Yang Winston C.
Published: January 2020

In two dimensions, a polyform is a finite set of edge-connected cells on a square, triangular, or hexagonal grid. A layer is the set of grid cells that are vertex-adjacent to the polyform and not part of the polyform. A bumped-body polyform has two parts: a body and a bump. Adding a layer to a bumped-body polyform with minimum perimeter constructs a bumped-body polyform with min perimeter; the triangle case requires additional assumptions. A similar result holds for 3D polyominos with minimum area.
More Forbidden Minors for Wye-Delta-Wye Reducibility
Authors: Yu Yaming
Published: January 2020

A graph is $Y\Delta Y$ reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and $Y\Delta Y$ transformations. It is still an open problem to characterize $Y\Delta Y$ reducible graphs in terms of a finite set of forbidden minors. We obtain a characterization of such forbidden minors that can be written as clique $k$-sums for $k=1, 2, 3$. As a result we show constructively that the total number of forbidden minors is more than 68 billion up to isomorphism.
Descendants in Increasing Trees
Authors: Kuba Markus , Panholzer Alois
Published: January 2020

Simple families of increasing trees can be constructed from simply generated tree families, if one considers for every tree of size $n$ all its increasing labellings, i.$\,$e. labellings of the nodes by distinct integers of the set $\{1, \dots, n\}$ in such a way that each sequence of labels along any branch starting at the root is increasing. Three such tree families are of particular interest: recursive trees, plane-oriented recursive trees and binary increasing trees. We study the quantity number of descendants of node $j$ in a random tree of size $n$ and give closed formulæ for the probability distribution and all factorial moments for those subclass of tree families, which can be constructed via an insertion process. Furthermore limiting distribution results of this parameter are given.
Sets of Points Determining Only Acute Angles and Some Related Colouring Problems
Authors: Bevan David
Published: January 2020

We present both probabilistic and constructive lower bounds on the maximum size of a set of points ${\cal S} \subseteq {\Bbb R}^d$ such that every angle determined by three points in ${\cal S}$ is acute, considering especially the case ${\cal S} \subseteq\{0,1\}^d$. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.
Covering Codes for Hats-on-a-line
Authors: Aravamuthan Sarang , Lodha Sachin
Published: January 2020

We consider a popular game puzzle, called Hats-on-a-line, wherein a warden has $n$ prisoners, each one wearing a randomly assigned black or white hat, stand in a line. Thus each prisoner can see the colors of all hats before him, but not his or of those behind him. Everyone can hear the answer called out by each prisoner. Based on this information and without any further communication, each prisoner has to call out his hat color starting from the back of the line. If he gets it right, he is released from the prison, otherwise he remains incarcerated forever. The goal of the team is to devise a strategy that maximizes the number of correct answers. A variation of this problem asks for the solution for an arbitrary number of colors. In this paper, we study the standard Hats-on-a-line problem and its natural extensions. We demonstrate an optimal strategy when the seeing radius and/or the hearing radius are limited. We show for certain orderings that arise from a (simulated) game between the warden and prisoners, how this problem relates to the theory of covering codes. Our investigations lead to two optimization problems related to covering codes in which one leads to an exact solution (for binary codes). For instance, we show that for $0 < k < n$, $(n-k-d) \le \alpha_m n$ where $d = t(n-k, m^k, m)$ is the minimum covering radius of an $m$-ary code of length ($n-k$) and size $m^k$ and $$\alpha_m = {\log m\over \log (m^2 -m +1)}.$$
An Alternative Definition of the Notion Valuation in the Theory of Near Polygons
Authors: De Bruyn Bart
Published: January 2020

Valuations of dense near polygons were introduced in [9]. A valuation of a dense near polygon ${\cal S}=({\cal P},{\cal L},{\rm I})$ is a map $f$ from the point-set ${\cal P}$ of ${\cal S}$ to the set $\Bbb N$ of nonnegative integers satisfying very nice properties with respect to the set of convex subspaces of ${\cal S}$. In the present paper, we give an alternative definition of the notion valuation and prove that both definitions are equivalent. In the case of dual polar spaces and many other known dense near polygons, this alternative definition can be significantly simplified.
Some Results on Odd Astral Configurations
Authors: Berman Leah Wrenn
Published: January 2020

An astral configuration $(p_q, n_k)$ is a collection of $p$ points and $n$ straight lines in the Euclidean plane where every point has $q$ straight lines passing through it and every line has $k$ points lying on it, with precisely $\lfloor {q+1\over 2} \rfloor$ symmetry classes (transitivity classes) of lines and $\lfloor {k+1\over 2} \rfloor$ symmetry classes of points. An odd astral configuration is an astral configuration where at least one of $q$ and $k$ is odd. This paper presents all known results in the classification of odd astral configurations where $q$ and $k$ are both at least 4.
Distribution of Crossings, Nestings and Alignments of Two Edges in Matchings and Partitions
Authors: Kasraoui Anisse , Zeng Jiang
Published: January 2020

We construct an involution on set partitions which keeps track of the numbers of crossings, nestings and alignments of two edges. We derive then the symmetric distribution of the numbers of crossings and nestings in partitions, which generalizes a recent result of Klazar and Noy in perfect matchings. By factorizing our involution through bijections between set partitions and some path diagrams we obtain the continued fraction expansions of the corresponding ordinary generating functions.
Automorphism Groups of Wreath Product Digraphs
Authors: Dobson Edward , Morris Joy
Published: January 2020

We generalize a classical result of Sabidussi that was improved by Hemminger, to the case of directed color graphs. The original results give a necessary and sufficient condition on two graphs, $C$ and $D$, for the automorphsim group of the wreath product of the graphs, ${\rm Aut}(C\wr D)$ to be the wreath product of the automorphism groups ${\rm Aut}(C)\wr {\rm Aut}(D)$. Their characterization generalizes directly to the case of color graphs, but we show that there are additional exceptional cases in which either $C$ or $D$ is an infinite directed graph. Also, we determine what ${\rm Aut}(C \wr D)$ is if ${\rm Aut}(C \wr D) \neq {\rm Aut} (C) \wr {\rm Aut} (D)$, and in particular, show that in this case there exist vertex-transitive graphs $C'$ and $D'$ such that $C' \wr D' = C \wr D$ and ${\rm Aut} (C\wr D) = {\rm Aut} (C') \wr {\rm Aut}(D')$.
Optimal Penney Ante Strategy via Correlation Polynomial Identities
Authors: Felix Daniel
Published: January 2020

In the game of Penney Ante two players take turns publicly selecting two distinct words of length $n$ using letters from an alphabet $\Omega$ of size $q$. They roll a fair $q$ sided die having sides labelled with the elements of $\Omega$ until the last $n$ tosses agree with one player's word, and that player is declared the winner. For $n\geq 3$ the second player has a strategy which guarantees strictly better than even odds. Guibas and Odlyzko have shown that the last $n-1$ letters of the second player's optimal word agree with the initial $n-1$ letters of the first player's word. We offer a new proof of this result when $q \geq 3$ using correlation polynomial identities, and we complete the description of the second player's best strategy by characterizing the optimal leading letter. We also give a new proof of their conjecture that for $q=2$ this optimal strategy is unique, and we provide a generalization of this result to higher $q$.
A Gessel–Viennot-Type Method for Cycle Systems in a Directed Graph
Authors: Hanusa Christopher R. H.
Published: January 2020

We introduce a new determinantal method to count cycle systems in a directed graph that generalizes Gessel and Viennot's determinantal method on path systems. The method gives new insight into the enumeration of domino tilings of Aztec diamonds, Aztec pillows, and related regions.
Tensorial Square of the Hyperoctahedral Group Coinvariant Space
Authors: Bergeron François , Biagioli Riccardo
Published: January 2020

The purpose of this paper is to give an explicit description of the trivial and alternating components of the irreducible representation decomposition of the bigraded module obtained as the tensor square of the coinvariant space for hyperoctahedral groups.
Optimal Four-Dimensional Codes over GF(8)
Authors: Jones Chris , Matney Angela , Ward Harold
Published: January 2020

We prove the nonexistence of several four-dimensional codes over GF(8) that meet the Griesmer bound. The proofs use geometric methods based on the analysis of the weight structure of subcodes. The specific parameters of the codes ruled out are: $[111,4,96],\,$ $[110,4,95],\,$ $[102,4,88],\,$ $[101,4,87],\,$ $[93,4,80],\,$ and the sequence $[29-j,4,24-j]$, for $j=0,1,2$.
Tilings of the Sphere with Right Triangles II: The $(1,3,2)$, $(0,2,n)$ Subfamily
Authors: Dawson Robert J. MacG. , Doyle Blair
Published: January 2020

Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper shows that no right triangles in a certain subfamily can tile the sphere, although multilayered tilings are possible.
Grid Classes and the Fibonacci Dichotomy for Restricted Permutations
Authors: Huczynska Sophie , Vatter Vincent
Published: January 2020

We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof of the Fibonacci dichotomy: the number of permutations of length $n$ in a permutation class is either at least as large as the $n$th Fibonacci number or is eventually polynomial.
Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities
Authors: Šniady Piotr
Published: January 2020

In this series of articles we study connections between combinatorics of multidimensional generalizations of the Cauchy identity and continuous objects such as multidimensional Brownian motions and Brownian bridges. In Part I of the series we present a bijective proof of the multidimensional generalizations of the Cauchy identity. Our bijection uses oriented planar trees equipped with some linear orders.
On Oriented Arc-Coloring of Subcubic Graphs
Authors: Pinlou Alexandre
Published: January 2020

A homomorphism from an oriented graph $G$ to an oriented graph $H$ is a mapping $\varphi$ from the set of vertices of $G$ to the set of vertices of $H$ such that $\overrightarrow{\varphi(u)\varphi(v)}$ is an arc in $H$ whenever $\overrightarrow{uv}$ is an arc in $G$. The oriented chromatic index of an oriented graph $G$ is the minimum number of vertices in an oriented graph $H$ such that there exists a homomorphism from the line digraph $LD(G)$ of $G$ to $H$ (Recall that $LD(G)$ is given by $V(LD(G))=A(G)$ and $ \overrightarrow{ab}\in A(LD(G))$ whenever $a=\overrightarrow{uv}$ and $b=\overrightarrow{vw}$). We prove that every oriented subcubic graph has oriented chromatic index at most $7$ and construct a subcubic graph with oriented chromatic index $6$.
Drawing a Graph in a Hypercube
Authors: Wood David R.
Published: January 2020

A $d$-dimensional hypercube drawing of a graph represents the vertices by distinct points in $\{0,1\}^d$, such that the line-segments representing the edges do not cross. We study lower and upper bounds on the minimum number of dimensions in hypercube drawing of a given graph. This parameter turns out to be related to Sidon sets and antimagic injections.
Identifying Graph Automorphisms Using Determining Sets
Authors: Boutin Debra L.
Published: January 2020

A set of vertices $S$ is a determining set for a graph $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The determining number of a graph is the size of a smallest determining set. This paper describes ways of finding and verifying determining sets, gives natural lower bounds on the determining number, and shows how to use orbits to investigate determining sets. Further, determining sets of Kneser graphs are extensively studied, sharp bounds for their determining numbers are provided, and all Kneser graphs with determining number $2$, $3,$ or $4$ are given.
Binary Words Containing Infinitely Many Overlaps
Authors: Currie James , Rampersad Narad , Shallit Jeffrey
Published: January 2020

We characterize the squares occurring in infinite overlap-free binary words and construct various $\alpha$ power-free binary words containing infinitely many overlaps.
Matchings Avoiding Partial Patterns and Lattice Paths
Authors: Jelínek Vít , Li Nelson Y. , Mansour Toufik , Yan Sherry H. F.
Published: January 2020

In this paper, we consider matchings avoiding partial patterns $1123$ and $1132$. We give a bijection between $1123$-avoiding matchings with $n$ edges and nonnegative lattice paths from $(0,2)$ to $(2n,0)$. As a consequence, the refined enumeration of $1123$-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a bijection between $1132$-avoiding matchings with $n$ edges and lattice paths from $(0,0)$ to $(2n,0)$ starting with an up step, which may go under the $x$-axis.
A Quantitative Ergodic Theory Proof of Szemerédi's Theorem
Authors: Tao Terence
Published: January 2020

A famous theorem of Szemerédi asserts that given any density $0 < \delta \leq 1$ and any integer $k \geq 3$, any set of integers with density $\delta$ will contain infinitely many proper arithmetic progressions of length $k$. For general $k$ there are essentially four known proofs of this fact; Szemerédi's original combinatorial proof using the Szemerédi regularity lemma and van der Waerden's theorem, Furstenberg's proof using ergodic theory, Gowers' proof using Fourier analysis and the inverse theory of additive combinatorics, and the more recent proofs of Gowers and Rödl-Skokan using a hypergraph regularity lemma. Of these four, the ergodic theory proof is arguably the shortest, but also the least elementary, requiring passage (via the Furstenberg correspondence principle) to an infinitary measure preserving system, and then decomposing a general ergodic system relative to a tower of compact extensions. Here we present a quantitative, self-contained version of this ergodic theory proof, and which is "elementary" in the sense that it does not require the axiom of choice, the use of infinite sets or measures, or the use of the Fourier transform or inverse theorems from additive combinatorics. It also gives explicit (but extremely poor) quantitative bounds.
Shift Equivalence of P-finite Sequences
Authors: Kauers Manuel
Published: January 2020

We present an algorithm which decides the shift equivalence problem for P-finite sequences. A sequence is called P-finite if it satisfies a homogeneous linear recurrence equation with polynomial coefficients. Two sequences are called shift equivalent if shifting one of the sequences $s$ times makes it identical to the other, for some integer $s$. Our algorithm computes, for any two P-finite sequences, given via recurrence equation and initial values, all integers $s$ such that shifting the first sequence $s$ times yields the second.
Cycle Lengths in a Permutation are Typically Poisson
Authors: Granville Andrew
Published: January 2020

The set of cycle lengths of almost all permutations in $S_n$ are "Poisson distributed": we show that this remains true even when we restrict the number of cycles in the permutation. The formulas we develop allow us to also show that almost all permutations with a given number of cycles have a certain "normal order" (in the spirit of the Erdős-Turán theorem). Our results were inspired by analogous questions about the size of the prime divisors of "typical" integers.
Proof of the Razumov–Stroganov Conjecture for some Infinite Families of Link Patterns
Authors: Zinn-Justin P.
Published: January 2020

We prove the Razumov–Stroganov conjecture relating ground state of the $O(1)$ loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches, for which we use as key ingredient of the proof a generalization of the MacMahon formula for the number of plane partitions which includes three series of parameters.
Restrictions and Generalizations on Comma-Free Codes
Authors: Churchill Alexander L.
Published: January 2020

A significant sector of coding theory is that of comma-free coding; that is, codes which can be received without the need of a letter used for word separation. The major difficulty is in finding bounds on the maximum number of comma-free words which can inhabit a dictionary. We introduce a new class called a self-reflective comma-free dictionary and prove a series of bounds on the size of such a dictionary based upon word length and alphabet size. We also introduce other new classes such as self-swappable comma-free codes and comma-free codes in q dimensions and prove preliminary bounds for these classes. Finally, we discuss the implications and applications of combining these original concepts, including their implications for the NP-complete Post Correspondence Problem.
The Non-Crossing Graph
Authors: Linial Nathan , Saks Michael , Statter David
Published: January 2020

Two sets are non-crossing if they are disjoint or one contains the other. The non-crossing graph ${\rm NC}_n$ is the graph whose vertex set is the set of nonempty subsets of $[n]=\{1,\ldots,n\}$ with an edge between any two non-crossing sets. Various facts, some new and some already known, concerning the chromatic number, fractional chromatic number, independence number, clique number and clique cover number of this graph are presented. For the chromatic number of this graph we show: $$ n(\log_e n -\Theta(1)) \le \chi({\rm NC}_n) \le n (\lceil\log_2 n\rceil-1). $$
A Note on the Number of Hamiltonian Paths in Strong Tournaments
Authors: Busch Arthur H.
Published: January 2020

We prove that the minimum number of distinct hamiltonian paths in a strong tournament of order $n$ is $5^{{n-1}\over{3}}$. A known construction shows this number is best possible when $n \equiv 1 \hbox{ mod } 3$ and gives similar minimal values for $n$ congruent to $0$ and $2$ modulo $3$.
Proof of an Intersection Theorem via Graph Homomorphisms
Authors: Dinur Irit , Friedgut Ehud
Published: January 2020

Let $0 \leq p \leq 1/2 $ and let $\{0,1\}^n$ be endowed with the product measure $\mu_p$ defined by $\mu_p(x)=p^{|x|}(1-p)^{n-|x|}$, where $|x|=\sum x_i$. Let $I \subseteq \{0,1\}^n$ be an intersecting family, i.e. for every $x, y \in I$ there exists a coordinate $1 \leq i \leq n$ such that $x_i=y_i=1$. Then $\mu_p(I) \leq p.$ Our proof uses measure preserving homomorphisms between graphs.
Dynamic Single-Pile Nim Using Multiple Bases
Authors: Holshouser Arthur , Reiter Harold
Published: January 2020

In the game $G_{0}$ two players alternate removing positive numbers of counters from a single pile and the winner is the player who removes the last counter. On the first move of the game, the player moving first can remove a maximum of $k$ counters, $k$ being specified in advance. On each subsequent move, a player can remove a maximum of $f(n,t) $ counters where $t$ was the number of counters removed by his opponent on the preceding move and $n$ is the preceding pile size, where $f:N\times N\rightarrow N$ is an arbitrary function satisfying the condition (1): $\exists t\in N$ such that for all $n,x\in N$, $f(n,x) =f(n+t,x) $. This note extends our earlier paper [E-JC, Vol 10, 2003, N7]. We first solve the game for functions $f:N\times N\rightarrow N$ that also satisfy the condition (2): $\forall n,x\in N$, $f(n,x+1) -f(n,x) \geq -1$. Then we state the solution when $f:N\times N\rightarrow N$ is restricted only by condition (1) and point out that the more general proof is almost the same as the simpler proof. The solutions when $t\geq 2$ use multiple bases.
Reachability Relations and the Structure of Transitive Digraphs
Authors: Seifter Norbert , Trofimov Vladimir I.
Published: January 2020

In this paper we investigate reachability relations on the vertices of digraphs. If $W$ is a walk in a digraph $D$, then the height of $W$ is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed opposite to their orientation. Two vertices $u,v\in V(D)$ are $R_{a,b}$-related if there exists a walk of height $0$ between $u$ and $v$ such that the height of every subwalk of $W$, starting at $u$, is contained in the interval $[a,b]$, where $a$ ia a non-positive integer or $a=-\infty$ and $b$ is a non-negative integer or $b=\infty$. Of course the relations $R_{a,b}$ are equivalence relations on $V(D)$. Factorising digraphs by $R_{a,\infty}$ and $R_{-\infty,b}$, respectively, we can only obtain a few different digraphs. Depending upon these factor graphs with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ it is possible to define five different "basic relation-properties" for $R_{-\infty,b}$ and $R_{a,\infty}$, respectively. Besides proving general properties of the relations $R_{a,b}$, we investigate the question which of the "basic relation-properties" with respect to $R_{-\infty,b}$ and $R_{a,\infty}$ can occur simultaneously in locally finite connected transitive digraphs. Furthermore we investigate these properties for some particular subclasses of locally finite connected transitive digraphs such as Cayley digraphs, digraphs with one, with two or with infinitely many ends, digraphs containing or not containing certain directed subtrees, and highly arc transitive digraphs.
Noncrossing Trees and Noncrossing Graphs
Authors: Chen William Y. C. , Yan Sherry H. F.
Published: January 2020

We give a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation of a formula on noncrossing trees and symmetric ternary trees in answer to a problem proposed by Hough. We use the representation of Panholzer and Prodinger for noncrossing trees and find a correspondence between a class of noncrossing trees, called proper noncrossing trees, and the set of symmetric ternary trees. The second result of this paper is a parity reversing involution on connected noncrossing graphs which leads to a relation between the number of noncrossing trees with $n$ edges and $k$ descents and the number of connected noncrossing graphs with $n+1$ vertices and $m$ edges.
The Induced Subgraph Order on Unlabelled Graphs
Authors: Sloss Craig A.
Published: January 2020

A differential poset is a partially ordered set with raising and lowering operators $U$ and $D$ which satisfy the commutation relation $DU-UD=rI$ for some constant $r$. This notion may be generalized to deal with the case in which there exist sequences of constants $\{q_n\}_{n\geq 0}$ and $\{r_n\}_{n\geq 0}$ such that for any poset element $x$ of rank $n$, $DU(x) = q_n UD(x) + r_nx$. Here, we introduce natural raising and lowering operators such that the set of unlabelled graphs, ordered by $G\leq H$ if and only if $G$ is isomorphic to an induced subgraph of $H$, is a generalized differential poset with $q_n=2$ and $r_n = 2^n$. This allows one to apply a number of enumerative results regarding walk enumeration to the poset of induced subgraphs.
The Circular Chromatic Index of Flower Snarks
Authors: Ghebleh Mohammad , Král' Daniel , Norine Serguei , Thomas Robin
Published: January 2020

We determine the circular chromatic index of flower snarks, by showing that $\chi'_c(F_{3})=7/2$, $\chi'_c(F_{5})=17/5$ and $\chi'_c(F_{k})=10/3$ for every odd integer $k\ge 7$, where $F_k$ denotes the flower snark on $4k$ vertices.
A New Table of Constant Weight Codes of Length Greater than 28
Authors: Smith D. H. , Hughes L. A. , Perkins S.
Published: January 2020

Existing tables of constant weight codes are mainly confined to codes of length $n\leq 28$. This paper presents tables of codes of lengths $29 \leq n \leq 63$. The motivation for creating these tables was their application to the generation of good sets of frequency hopping lists in radio networks. The complete generation of all relevant cases by a small number of algorithms is augmented in individual cases by miscellaneous constructions. These sometimes give a larger number of codewords than the algorithms.
The Smallest One-Realization of a Given Set
Authors: Zhao Ping , Diao Kefeng , Wang Kaishun
Published: January 2020

For any set $S$ of positive integers, a mixed hypergraph ${\cal H}$ is a realization of $S$ if its feasible set is $S$, furthermore, ${\cal H}$ is a one-realization of $S$ if it is a realization of $S$ and each entry of its chromatic spectrum is either 0 or 1. Jiang et al. showed that the minimum number of vertices of a realization of $\{s,t\}$ with $2\leq s\leq t-2$ is $2t-s$. Král proved that there exists a one-realization of $S$ with at most $|S|+2\max{S}-\min{S}$ vertices. In this paper, we  determine the number  of vertices of the smallest one-realization of a given set. As a result, we partially solve an open problem proposed by Jiang et al. in 2002 and by Král  in 2004.
Symmetric Chain Decomposition of Necklace Posets
Authors: Dhand Vivek
Published: January 2020

A finite ranked poset is called a symmetric chain order if it can be written as a disjoint union of rank-symmetric, saturated chains. If $\mathcal{P}$ is any symmetric chain order, we prove that $\mathcal{P}^n/\mathbb{Z}_n$ is also a symmetric chain order, where $\mathbb{Z}_n$ acts on $\mathcal{P}^n$ by cyclic permutation of the factors.
A Recurrence for Counting Graphical Partitions
Authors: Barnes Tiffany M. , Savage Carla D.
Published: January 2020

In this paper, we give a recurrence to enumerate the set $G(n)$ of partitions of a positive even integer $n$ which are the degree sequences of simple graphs. The recurrence gives rise to an algorithm to compute the number of elements of $G(n)$ in time $O(n^4)$ using space $O(n^3)$. This appears to be the first method for computing $|G(n)|$ in time bounded by a polynomial in $n$, and it has enabled us to tabulate $|G(n)|$ for even $n \leq 220$.
Enumeration of Derangements with Descents in Prescribed Positions
Authors: Eriksen Niklas , Freij Ragnar , Wästlund Johan
Published: January 2020

We enumerate derangements with descents in prescribed positions. A generating function was given by Guo-Niu Han and Guoce Xin in 2007. We give a combinatorial proof of this result, and derive several explicit formulas. To this end, we consider fixed point $\lambda$-coloured permutations, which are easily enumerated. Several formulae regarding these numbers are given, as well as a generalisation of Euler's difference tables. We also prove that except in a trivial special case, if a permutation $\pi$ is chosen uniformly among all permutations on $n$ elements, the events that $\pi$ has descents in a set $S$ of positions, and that $\pi$ is a derangement, are positively correlated.
Line-transitive Automorphism Groups of Linear Spaces
Authors: Camina Alan R , Mischke Susanne
Published: January 2020

In this paper we prove the following theorem. Let $\cal S$ be a linear space. Assume that $\cal S$ has an automorphism group $G$ which is line-transitive and point-imprimitive with $k < 9$. Then $\cal S$ is one of the following:- (a) A projective plane of order $4$ or $7$, (b) One of $2$ linear spaces with $v=91$ and $k=6$, (c) One of $467$ linear spaces with $v=729$ and $k=8$. In all cases the full automorphism group Aut(${\cal S} \!$) is known.
The Number of Knight's Tours Equals 33,439,123,484,294 — Counting with Binary Decision Diagrams
Authors: Löbbing Martin , Wegener Ingo
Published: January 2020

The number of knight's tours, i.e. Hamiltonian circuits, on an $8 \times 8$ chessboard is computed with decision diagrams which turn out to be a useful tool for counting problems.
The Existence of FGDRP$(3,g^u)'$s
Authors: Yan Jie , Wang Chengmin
Published: January 2020

By an FGDRP$(3,g^u)$, we mean a uniform frame $(X,\cal G,\cal A)$ of block size 3, index 2 and type $g^u$, where the blocks of $\cal{A}$ can be arranged into a $gu/3\times gu$ array. This array has the properties: (1) the main diagonal consists of $u$ empty subarrays of sizes $g/3\times g$; (2) the blocks in each column form a partial parallel class partitioning $X \setminus G$ for some $G\in \cal G$, while the blocks in each row contain every element of $X \setminus G$ $3$ times and no element of $G$ for some $G\in \cal{G}$. The obvious necessary conditions for the existence of an FGDRP$(3,g^u)$ are $u\geq 5$ and $g\equiv 0$ (mod 3). In this paper, we show that these conditions are also sufficient with the possible exceptions of $(g,u)\in \{(6,15),(9,18),(9,28),(9,34),(30,15)\}$.
Applying Tabu Search to Determine New Ramsey Graphs
Authors: Piwakowski Konrad
Published: January 2020

In this note an adaptation of heuristic tabu search algorithm for finding Ramsey graphs is presented. As a result, seven new lower bounds for classical Ramsey numbers are established: $R(3,13)\geq 59$, $R(4,10)\geq 80$, $R(4,11)\geq 96$, $R(4,12)\geq 106$, $R(4,13)\geq 118$, $R(4,14)\geq 129$, and $R(5,8)\geq 95$.
An improved tableau criterion for Bruhat order
Authors: Björner Anders , Brenti Francesco
Published: January 2020

To decide whether two permutations are comparable in Bruhat order of $S_n$ with the well-known tableau criterion requires $\binom{n}{2}$ comparisons of entries in certain sorted arrays. We show that to decide whether $x\le y$ only $d_1+d_2+...+d_k$ of these comparisons are needed, where $\{d_1,d_2,...,d_k\} = \{i|x(i)>x(i+1)\}$. This is obtained as a consequence of a sharper version of Deodhar's criterion, which is valid for all Coxeter groups.