bluuebunny/crossref_metadata_2025_split huggingface dataset:
Arc-Transitive Dihedral Regular Covers of Cubic Graphs
Authors: Ma Jicheng 
Published: January 2020

A regular covering projection is called dihedral or abelian if the covering transformation group is dihedral or abelian. A lot of work has been done with regard to the classification of arc-transitive abelian (or elementary abelian, or cyclic) covers of symmetric graphs. In this paper, we investigate arc-transitive dihedral regular covers of symmetric (arc-transitive) cubic graphs. In particular, we classify all arc-transitive dihedral regular covers of $K_4$, $K_{3,3}$, the 3-cube $Q_3$ and the Petersen graph.
Sandpiles and Dominos
Authors: Florescu Laura , Morar Daniela , Perkinson David , Salter Nicholas , Xu Tianyuan 
Published: January 2020

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product whose factors are sums of squares of values of trigonometric functions. We provide a new derivation of the formula due to Kasteleyn and to Temperley and Fisher for counting the number of domino tilings of a $2m \times 2n$ rectangular checkerboard and a new way of counting the number of domino tilings of a $2m \times 2n$ checkerboard on a Möbius strip.
A Note on Statistical Averages for Oscillating Tableaux
Authors: Hopkins Sam , Zhang Ingrid 
Published: January 2020

Oscillating tableaux are certain walks in Young's lattice of partitions; they generalize standard Young tableaux. The shape of an oscillating tableau is the last partition it visits and the length of an oscillating tableau is the number of steps it takes. We define a new statistic for oscillating tableaux that we call weight: the weight of an oscillating tableau is the sum of the sizes of all the partitions that it visits. We show that the average weight of all oscillating tableaux of shape $\lambda$ and length $|\lambda|+2n$ (where $|\lambda|$ denotes the size of $\lambda$ and $n \in \mathbb{N}$) has a surprisingly simple formula: it is a quadratic polynomial in $|\lambda|$ and $n$. Our proof via the theory of differential posets is largely computational. We suggest how the homomesy paradigm of Propp and Roby may lead to a more conceptual proof of this result and reveal a hidden symmetry in the set of perfect matchings.
Characteristic Flows on Signed Graphs and Short Circuit Covers
Authors: Máčajová Edita , Škoviera Martin 
Published: January 2020

We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8 (1956), 13—28] stating that every integer flow can be expressed as a sum of characteristic flows of circuits. In our generalisation, the rôle of circuits is taken over by signed circuits of a signed graph which occur in two types — either balanced circuits or pairs of disjoint unbalanced circuits connected with a path intersecting them only at its ends. As an application of this result we show that a signed graph $G$ admitting a nowhere-zero $k$-flow has a covering with signed circuits of total length at most $2(k-1)|E(G)|$.
Polynomials Defined by Tableaux and Linear Recurrences
Authors: Alexandersson Per 
Published: January 2020

We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials, (also known as Demazure characters), and Demazure atoms. The same technique can be applied to Hall-Littlewood polynomials and dual Grothendieck polynomials.The motivation behind this is that such recurrences are strongly connected with other nice properties, such as interpretations in terms of lattice points in polytopes and divided difference operators.
On the Staircases of Gyárfás
Authors: Csányi János , Hajnal Peter , Nagy Gábor V. 
Published: January 2020

In a 2011 paper, Gyárfás investigated a geometric Ramsey problem on convex, separated, balanced, geometric $K_{n,n}$. This led to appealing extremal problem on square 0-1 matrices. Gyárfás conjectured that any 0-1 matrix of size $n\times n$ has a staircase of size $n-1$.We introduce the non-symmetric version of Gyárfás' problem. We give upper bounds and in certain range matching lower bound on the corresponding extremal function. In the square/balanced case we improve the $(4/5+\epsilon)n$ lower bound of Cai, Gyárfás et al. to $5n/6-7/12$. We settle the problem when instead of considering maximum staircases we deal with the sum of the size of the longest $0$- and $1$-staircases.
Infinite Excursions of Rotor Walks on Regular Trees
Authors: Müller Sebastian , Orenshtein Tal 
Published: January 2020

A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a deterministic process: at each step it chooses the next unused rotor in its current location, and uses it to jump to the neighboring vertex to which it points. Rotor walks capture many aspects of the expected behavior of simple random walks. However, this similarity breaks down for the property of having an infinite excursion. In this paper we study that question for natural random configuration models on regular trees. Our results suggest that in this context the rotor model behaves like the simple random walk unless it is not "close to" the standard rotor-router model.
Small Subgraphs in the Trace of a Random Walk
Authors: Krivelevich Michael , Michaeli Peleg 
Published: January 2020

We consider the combinatorial properties of the trace of a random walk on the complete graph and on the random graph $G(n,p)$. In particular, we study the appearance of a fixed subgraph in the trace. We prove that for a subgraph containing a cycle, the threshold for its appearance in the trace of a random walk of length $m$ is essentially equal to the threshold for its appearance in the random graph drawn from $G(n,m)$. In the case where the base graph is the complete graph, we show that a fixed forest appears in the trace typically much earlier than it appears in $G(n,m)$.
Forbidden Pairs with a Common Graph Generating Almost the Same Sets
Authors: Chiba Shuya , Fujisawa Jun , Furuya Michitaka , Ikarashi Hironobu 
Published: January 2020

Let $\mathcal{H}$ be a family of connected graphs. A graph $G$ is said to be $\mathcal{H}$-free if $G$ does not contain any members of $\mathcal{H}$ as an induced subgraph. Let $\mathcal{F}(\mathcal{H})$ be the family of connected $\mathcal{H}$-free graphs. In this context, the members of $\mathcal{H}$ are called forbidden subgraphs.In this paper, we focus on two pairs of forbidden subgraphs containing a common graph, and compare the classes of graphs satisfying each of the two forbidden subgraph conditions. Our main result is the following: Let $H_{1},H_{2},H_{3}$ be connected graphs of order at least three, and suppose that $H_{1}$ is twin-less. If the symmetric difference of $\mathcal{F}(\{H_{1},H_{2}\})$ and $\mathcal{F}(\{H_{1},H_{3}\})$ is finite and the tuple $(H_{1};H_{2},H_{3})$ is non-trivial in a sense, then $H_{2}$ and $H_{3}$ are obtained from the same vertex-transitive graph by successively replacing a vertex with a clique and joining the neighbors of the original vertex and the clique. Furthermore, we refine a result in [Combin. Probab. Comput. 22 (2013) 733–748] concerning forbidden pairs.
The Gorenstein Property for Projective Coordinate Rings of the Moduli of Parabolic $\mathrm{SL}_2$-Principal Bundles on a Smooth Curve
Authors: Faust Theodore , Manon Christopher 
Published: January 2020

Using combinatorial methods, we determine that a projective coordinate ring of the moduli of parabolic principal $\mathrm{SL}_2-$bundles on a marked projective curve is not Gorenstein when the genus and number of marked points are greater than $1$.
On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture
Authors: Asada Megumi , Chen Ryan , Frick Florian , Huang Frederick , Polevy Maxwell , Stoner David , Tsang Ling Hei , Wellner Zoe 
Published: January 2020

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.
Every Plane Graph is Facially-Non-Repetitively $C$-choosable
Authors: Gutowski Grzegorz 
Published: January 2020

A sequence $\left(x_1,x_2,\ldots,x_{2n}\right)$ of even length is a repetition if $\left(x_1,\ldots,x_n\right) =\left(x_{n+1},\ldots,x_{2n}\right)$. We prove existence of a constant $C < 10^{4 \cdot 10^7}$ such that given any planar drawing of a graph $G$, and a list $L(v)$ of $C$ permissible colors for each vertex $v$ in $G$, there is a choice of a permissible color for each vertex such that the sequence of colors of the vertices on any facial simple path in $G$ is not a repetition.
Path Choosability of Planar Graphs
Authors: Chappell Glenn G. , Hartman Chris 
Published: January 2020

A path coloring of a graph $G$ is a vertex coloring of $G$ such that each color class induces a disjoint union of paths. We consider a path-coloring version of list coloring for planar and outerplanar graphs. We show that if each vertex of a planar graph is assigned a list of $3$ colors, then the graph admits a path coloring in which each vertex receives a color from its list. We prove a similar result for outerplanar graphs and lists of size $2$.For outerplanar graphs we prove a multicoloring generalization. We assign each vertex of a graph a list of $q$ colors. We wish to color each vertex with $r$ colors from its list so that, for each color, the set of vertices receiving it induces a disjoint union of paths. We show that we can do this for all outerplanar graphs if and only if $q/r \ge 2$. For planar graphs we conjecture that a similar result holds with $q/r \ge 3$; we present partial results toward this conjecture.
Lozenge Tilings of a Halved Hexagon with an Array of Triangles Removed from the Boundary, Part II
Authors: Lai Tri 
Published: January 2020

Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later extended this tiling enumeration to a halved hexagon with a triangle cut off from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of triangles has been removed from the staircase side of the halved hexagon. Our result also implies an explicit formula for the number of tilings of a hexagon with an array of triangles removed perpendicularly to the symmetry axis.
On Monochromatic Pairs of Nondecreasing Diameters
Authors: O'Neal Adam , Schroeder Michael W. 
Published: January 2020

Let $n$, $m$, $r$, $t$ be positive integers and $\Delta:[n]\to[r]$. We say $\Delta$ is $(m,r,t)$-permissible if there exist $t$ disjoint $m$-sets $B_1,\dots,B_t$ contained in $[n]$ for which

$|\Delta(B_i)|=1$ for each $i=1,2,\dots,t$,
$\max(B_i) < \min(B_{i+1})$ for each $i=1,2,\dots,t-1$, and
$\max(B_i)-\min(B_i) \leq \max(B_{i+1})-\max(B_{i+1})$ for each $i=1,2,\dots,t-1$.

Let $f(m,r,t)$ be the smallest such $n$ so that all colorings $\Delta$ are $(m,r,t)$-permissible. In this paper, we show that $f(2,2,t)=5t-4$.
Uniform Generation of Spanning Regular Subgraphs of a Dense Graph
Authors: Gao Pu , Greenhill Catherine 
Published: January 2020

Let $H_n$ be a graph on $n$ vertices and let $\overline{H_n}$ denote the complement of $H_n$. Suppose that $\Delta = \Delta(n)$ is the maximum degree of $\overline{H_n}$. We analyse three algorithms for sampling $d$-regular subgraphs ($d$-factors) of $H_n$. This is equivalent to uniformly sampling $d$-regular graphs which avoid a set $E(\overline{H_n})$ of forbidden edges. Here $d=d(n)$ is a positive integer which may depend on $n$.
Two of these algorithms produce a uniformly random $d$-factor of $H_n$ in expected runtime which is linear in $n$ and low-degree polynomial in $d$ and $\Delta$. The first algorithm applies when $(d+\Delta)d\Delta = o(n)$. This improves on an earlier algorithm by the first author, which required constant $d$ and at most a linear number of edges in $\overline{H_n}$. The second algorithm applies when $H_n$ is regular and $d^2+\Delta^2 = o(n)$, adapting an approach developed by the first author together with Wormald. The third algorithm is a simplification of the second, and produces an approximately uniform $d$-factor of $H_n$ in time $O(dn)$. Here the output distribution differs from uniform by $o(1)$ in total variation distance, provided that $d^2+\Delta^2 = o(n)$.
PENDIDIKAN KARAKTER DALAM KAJIAN FILSAFAT NILAI
Authors: Ida Rochmawat  
Published: January 2020

The main goal of becoming human character education in Indonesia. Character
education that proclaimed nationally and massif in
all levels of education to this
point so that learners have a superior character. The application of character
education that has gone on for many years such has been his impact can be felt or
is only limited to the theory presented in front of the class
and become the motto
in schools. In the view of philosophy of value, character education is the
cultivation of the values that will be embedded in the inside. In Indonesia, it is
character education who wish to apply should be tailored to the purpose of
ed
ucation nationally with a system of values that already exist in the community.
Among the many values that thrive in the community, in fact Indonesia nation
already has the basics of value yanag bermsyarakat life ilandasaan, became a
nation and a country
PENGEMBANGAN LEMBAR KERJA SISWA (LKS) IPA BERBASIS PhET “ OPTICAL GEOMETRI ” TEMA MATA
Authors: Idzi’ Layyinai  
Published: January 2020

Abstract
:
Developmental
research already been done by
the
title “Development
of Student
Work Sheet
Science
basis
on
PhET
”Optical Geometri”
T
heme eye.”. This research intent to describe
work sheet
student
feasibility gets basis PhET “Optical is Geometry”
theme
eye
to be sighte
d bases material
component criterion, representation, and language; feasibility is sighted from student response. This
research points on developmental model 4D but then just come up develop (development). Anal
yze of
the
research was done by descriptive q
uantitative, one that points out that
Student
Work Sheet gets basis
PhET was reasonable being utilized deep learning is sighted of all aspect covers material with
percentage as big as 88.88%, representation as big as 88.88%, and language as big as 85.00%.
Besides
feasibility also being sighted of student response that cover representation feasibility in learning as big as
93.42%, Representation criterion
of Student
Work Sheet as big as 80.26%, and language as big as
75.43%
.
Learned thoroughness individua
lly with percenta
s
e as big as 100% complete with
up to
KKM as
big as ≥ 70 and klasi
c
al
with percentase
100% complete as supporting as feasibiliti
Upaya Penjaminan Mutu Pendidikan Melalui Akreditasi Sekolah Di 9 SDN Di Wilayah Kabupaten Lamongan
Authors: Zainal Aqib  
Published: January 2020

Abstract:
Expedient in progress the National Education Quality in a order to hoped
that suitable with “UU No. 20 Th 2003” about the National Education system,
need to do improving all at once to constructive. The control education quality
system, that given with pass acridity. Acridity be held for constant the proper of
program and school education unite in every ladder and kind of education.
Acridity to program and education unite be held by national acridity board. Based
above, is “what with have school acridity can guarantee education quality in the
nine SDN in Lamongan regency?” The direction of observation is to give
information about the popper of school or program that to do standard national
education. If advantage that hoped from this result of PTS like statement for
school at expedient improving quality and program of improving school. The
observation be held at 9 SDN at July 2009 with use acridity instrument from BAN
S/M. The observation file be analysis based penscoran technique and progress the
result of acridity. This result of PTS is show there is improving value, from
sickles 1 and sickles II. The finally result show if the value acridity of 9 SDN, it is
about 71-85 with acridity average B. To headmaster, you must constant can
improving result acridity four years later.
mplementasi Metode Iqra’ Dan Metode Tilawati Dalam Pembelajaran Al-Qur’an Di Madrasah Diniyah Al-falah Modung Bangkalan
Authors: Subhan Adi Santoso  
Published: January 2020

Abstract:
The role of the Qur'an in guiding and directing human life, then
learning to read, understand and live the Qur'an to be practiced in everyday life is
a duty for every Muslim. But unfortunately, the current phenomenon is not so.
There are still many good Muslims from among children, adolescents, adults,
even parents can not read and write the letter of the Qur'an (illiteracy of the
Qur'an). Such a situation raises concerns especially for Muslims in Indonesia.
The author will choose the location of research at Madrasah Diniyah Al-falah
Modung Bangkalan. The subject of the research is the headmaster Waka
curriculum, Ustadz / dzh, and students. In this study the authors use three kinds of
data collection techniques that is the method of observation or observation,
interview method, documentation method. 1 Implementation of Iqra 'and Tilawati
methods in Madrasah Diniyah Al-Falah Modung Bangkalan such as: the use of
CBSA system (How to Study Active Students); the use of direct reading and
Individual reading techniques (reading individually in front of ustadz / ustadzah).
2 The implementation equation between Iqra 'and Tilawati methods are: the use
of CBSA system (Active Learning Student), the use of Direct Spelling technique in
its reading, the use of Individual technique (individual reading in front of ustadz /
ustadzah), and compiled / Variative. As for the difference in the implementation of
Iqra 'and Tilawati methods are: for the Tilawati method using the National
Standard Rost song, while for Iqra' method it is not allowed to use the song even
though Irott Murottal; in Iqra 'method using sound approach for difficult letters in
its pronunciation, whereas in Tilawati method it is emphasized to pronounce
letters according to the right makhraj; besides using Individual reading technique
on Tilawati method also using classical technique, whereas in Iqra 'method only
use Individual technique only. 3 Factors that support the implementation of Iqra
'and Tilawati methods in Madrasah Diniyah Al-Falah Modung Bangkalan,
namely: the availability of props and tapes Murottal (with some type of rhythm of
the song); to shorten the time, as long as Individual ustadz / ustadzah assisted by
an assistant so that the reading achievement of students can be monitored
maximally and santri have a lot of maximal learning time as well.
Modal Utama Agar Menjadi Guru Favorit Bagi Peserta Didiknya
Authors: Yazidul Busthomi  
Published: January 2020

Abstract: Being a teacher is a truly noble job. He is responsible not only to make
the intelligent human beings in the field of science, but also good moral in this
life. A human child who at first did not understand anything, in the presence of a
teacher educated to understand life better and get to know the world. On the
shoulders there are tasks and responsibilities for the future of a smarter and more
intelligent generation. So noble work of a teacher as well as how heavy the duties
and responsibilities of being a teacher. This is why not everyone can be a
successful teacher. Only certain people who have a sense of love for children or
learners and dedicated to the world of education are able to become a teacher.
This is the person of a teacher who successfully teaches and educates in front of
his students, the figure of a favorite teacher loved by his protege. The main capital
to be a favorite teacher for students that is as follows: 1. Close to students, 2.
Build a fun atmosphere, 3. Can play as a second parent, 4. Become a friend in
learning, 5. Personality worth imitating, 6. Be affectionate, 7. Patience in
teaching, 8. Not arrogant.
Meningkatkan Hasil Belajar Siswa Pada Notasi Sigma, Barisan Dan Deret Melalui Model Pembelajaran Kooperatif Tipe Jigsaw Di Kelas XII IPA I S ekolah M enengah A tas Negeri I Muaro Jambi
Authors: ANCE ERIPIANA TAMBUNAN  
Published: January 2020

Abstract
:
The math learning process in XII IPA SMAN 1 Muaro Jambi
had been run ineffectively that had affected on unsatitissfied learning’s result.
Besides, the laxk of students’ willing on learning were identifying through the
learning motivation, learning process
interaction dan students’ learning
readiness and the results of learning. This action reaseach purposes to
explore the Jigsaw model for cooperative learning is able to to improve
student’s learning result pn sigma notation concepts, sequences, and series.
This study conducted in XII 1PA 1 SMAN 1 Muaro Jambi in 3 phases. The
result of study shows that the Jigsaw model can improve learning process
whereas the first phase 20 students passed in learning, the second phase 25
students achieved the learning
score, and the last past 34 students rose the
learning score