bluuebunny/crossref_metadata_2025 huggingface dataset:
The Family as the Centre of Moral Values and Ethics: Challenges since the Covid-19 Pandemic
Authors: Mathipa Prof. E. R , Ramorola Prof. M. Z , Motsepe Dr. Q. M
Published: August 2021

Nation-states are a result of the existence of families which constitutes communities that form them. Therefore, without families, regardless of how developed they are, there can’t be communities, and, thus, no nation-states. Religiously argued, the family is the cardinal centre of focus when the wellbeing of a nation-state is to be assessed. Implying that, when families disintegrate, the survival of communities and of nations cannot be guaranteed. Precisely because of this, the family is a primary institution where religious, socio-economic and moral values are imparted to children who ultimately constitute future generations. To unravel dilemmas caused by the devastation of Covid19 pandemic on families, Maslow’s theory and also that of nihilism are utilised in tandem with the principles and values that are underpinned by Rossouw’s theory. The article aims to preserve the family as an important unit whose core functions is the production of communities. Religiously, diverse belief systems have from time immemorial used and or applied their principles and moral values to either overcome or manage dangers faced by families, or communities at large. Currently, the effects of Covid-19 on the economy, society, religious and learning institutions including essential establishments that delivers critical services are either under great pressure or have stopped functioning entirely. No question, Covid-19 is slowly but surely eroding and altering the way the world’s people are living. It has introduced modes of survival hitherto known or which were never practiced before.
BİTKİ AKTİVATÖRÜNÜN SORGUM-SUDAN OTU MELEZİ FARKLI UYGULAMALARININ VERİM VE VERİM UNSURLARINA ETKİSİ
Authors: Murat CANYİĞİT  , Mustafa OKANT
Published: August 2021

Araştırma, Şanlıurfa ekolojik koşullarında 2014-2015 üretim sezonu ikinci ürün tek biçimde (Megamineral) bitki aktivatörünün sorgum-sudanotu melezi çeşitlerinde (Sorghum bicolor x Sorghum sudanense) farklı uygulamalarının verim ve verim unsurlarına etkisinin incelenmesi amacıyla, Harran üniversitesi Eyyübiye kampüsü Tarla Bitkileri araştırma ve geliştirme arazisinde yürütülmüştür. Araştırmada toplam 2 farklı sorgum-sudanotu melezi çeşidi kullanılmış olup, tarla denemeleri tesadüf bloklarında bölünmüş parseller deneme desenine göre 3 tekerrürlü, 5 (0, 250, 500, 750, 1000 g/da) megamineral uygulama olarak kurulmuştur. (Her uygulama dozu bir önceki uygulamadan 10 gün sonra 250 g/da dozunda uygulanmıştır). Araştırmada; yeşil ot verimi, kuru ot verimi, ham protein oranı, bitki boyu (cm) ve yaprak oranı gibi bazı özellikler de incelenmiştir. Araştırma sonucuna göre; genotiplerin, bitki boyu değerleri sugargraze II 232.3-269.7 cm greengo 215.7-244.3 cm, yeşil ot verimi sugargraze II 4730,5-5622,4 kg/da greengo 4245,2-7033,4 kg/da, kuru ot verimi sugargraze II 2138,4-2908,1 kg/da greengo 2424,5-3850,1 kg/da, ham protein oranı sugargraze II % 12.1-9.1 greengo %10.7-13.1, yaprak oranı sugargrazeII %16.4-18.1 greengo %20.1-22.7 arasında değişim göstermiştir. Bu sonuçlara göre, Şanlıurfa ili iklim ve toprak koşullarında; silaj veya kaba yem üretim amacıyla ikinci ürün olarak sugargraze II çeşidi 4. megamineral uygulamasından greengo çeşidi 5. megamineral uygulamasından şeklinde yetiştirilmesi önerilir ve megamineralin sorgum-sudanotu melezlerinde çok biçim üzerinden çalışmalar yapılması tavsiye edilir.
SİS HASADI
Authors: Sinan ÖZCAN  , Mine PAKYÜREK
Published: August 2021

Dünyada son yıllarda yaşanan nüfus artışı ile birlikte yoğunlaşan sanayi sektörü, tarımsal faaliyetler ve iklim değişiklikleri gibi küresel stres senaryoları tatlı su kaynakları üzerinde nitelik ve nicelik açısından olumsuz etkilere neden olmaktadır. Günümüzde bu sebeple giderek azalan ve kötüleşen tatlı su kaynaklarına çözüm olabilecek alternatif tatlı su kaynaklarının geliştirilmesine ihtiyaç duyulmaktadır. Sisten su elde etmek esasına dayalı bir yöntem olan sis hasadı bu noktada dikkat çeken alternatif tatlı su üretim tekniklerinden biridir. Bu sistemler sis varlığının doğal olarak yüksek olduğu kıyı ve dağlık bölgelerde kurulmaktadır.  Sistemin çalışma prensibi sis toplayıcı bir panelin içinden sisin geçmesi ve bu panelin içinde bulunan ağlar tarafından sis suyunun toplanması esasına dayanmaktadır. Sis toplayıcı ağ doğrudan atmosfere maruz kalmakta ve sisli hava rüzgar yoluyla ağdan içeriye doğru itilmektedir. Sis damlacıkları ağ üzerinde yakalanarak daha büyük damlacıklar haline gelip bir depolama tankına aktarılır ve orada toplanır. Sis suyu toplama oranları bölgeden bölgeye önemli ölçüde değişiklik göstermekle beraber sis damlacıklarının toplanması damlacıkların çapına, rüzgar hızına ve toplama yüzeyinin yapısına bağlı olmaktadır. Sistemin başarısı ise en çok sis toplama kafesinin yapısı ve çeşidine bağlı olarak değişmektedir. Bu sistemlerde toplanan sis suyu miktarı ve kalitesine bağlı olarak sis hasadına yönelik projelerin sürdürebilirliği de günümüz araştırma konuları arasında yer almaktadır. Bu derleme makalesi, sis suyu hasadı için mevcut model ve tasarımları tespit etmek ve dünya genelinde sürdürülebilir bir tatlı su kaynağı olarak sis hasadının hangi parametrelere dayandığını araştırmak amacıyla hazırlanmıştır.
Scoliosis in Pediatric Patients With Acute Flaccid Myelitis
Authors: Suresh Krishna V. , Karius Alexander , Wang Kevin Y. , Sadowsky Cristina , Sponseller Paul D.
Published: August 2021

Background:

Acute flaccid myelitis (AFM) is an anterior horn disorder that manifests as rapid onset muscle weakness or paralysis. Development of scoliosis in pediatric AFM patients has been anecdotally reported, but associated risk factors or incidence have yet to be determined.

Methods:

Pediatric AFM patients treated over a 10-year period at a tertiary care center were identified. Patients were considered to have scoliosis if there was radiographic evidence of coronal curvature ≥15 degrees. Number of limbs affected, independent ambulation and head control, ventilator requirement at initial admission, and long-term ventilatory support (≥1 year) were recorded. Muscle strength and functional status were assessed by manual muscle testing (MMT) and Physical Abilities and Mobility Scale (PAMS), respectively. Areas of spinal cord lesion on initial MRI were recorded. Bivariate analyses were performed, with alpha set to 0.05.

Results:

Fifty-six AFM patients (27 scoliosis, 29 no scoliosis) were identified. Mean time from AFM presentation to scoliosis diagnosis was 0.93 years. Mean major Cobb angle at first radiograph was 31.7 ± 14.3 degrees. Lack of independent ambulation, ventilator dependence at time of admission or long term, number of limbs affected, and decreased MMT and PAMS scores were more common in patients who developed scoliosis (all, p < .05). Patients who developed scoliosis had more extensive thoracic spinal cord involvement on initial MRI (p = .03).

Conclusion:

AFM patients who develop scoliosis are more likely to be ventilator dependent, lack independent ambulation, and have more extensive thoracic SCI.
Sticky Seeding in Discrete-Time Reversible-Threshold Networks
Authors: Spencer Gwen
Published: August 2021

When nodes can repeatedly update their behavior (as in agent-based models
from computational social science or repeated-game play settings) the problem
of optimal network seeding becomes very complex. For a popular
spreading-phenomena model of binary-behavior updating based on thresholds of
adoption among neighbors, we consider several planning problems in the design
of \textit{Sticky Interventions}: when adoption decisions are reversible, the
planner aims to find a Seed Set where temporary intervention leads to long-term
behavior change. We prove that completely converting a network at minimum cost
is $\Omega(\ln (OPT) )$-hard to approximate and that maximizing conversion
subject to a budget is $(1-\frac{1}{e})$-hard to approximate. Optimization
heuristics which rely on many objective function evaluations may still be
practical, particularly in relatively-sparse networks: we prove that the
long-term impact of a Seed Set can be evaluated in $O(|E|^2)$ operations. For a
more descriptive model variant in which some neighbors may be more influential
than others, we show that under integer edge weights from $\{0,1,2,...,k\}$
objective function evaluation requires only $O(k|E|^2)$ operations. These
operation bounds are based on improvements we give for bounds on
time-steps-to-convergence under discrete-time reversible-threshold updates in
networks.
The Price of Connectivity for Vertex Cover
Authors: Camby Eglantine , Cardinal Jean , Fiorini Samuel , Schaudt Oliver
Published: August 2021

Graph Theory

The vertex cover number of a graph is the minimum number of vertices that are needed to cover all edges. When those vertices are further required to induce a connected subgraph, the corresponding number is called the connected vertex cover number, and is always greater or equal to the vertex cover number. Connected vertex covers are found in many applications, and the relationship between those two graph invariants is therefore a natural question to investigate. For that purpose, we introduce the \em Price of Connectivity, defined as the ratio between the two vertex cover numbers. We prove that the price of connectivity is at most 2 for arbitrary graphs. We further consider graph classes in which the price of connectivity of every induced subgraph is bounded by some real number t. We obtain forbidden induced subgraph characterizations for every real value t ≤q 3/2. We also investigate critical graphs for this property, namely, graphs whose price of connectivity is strictly greater than that of any proper induced subgraph. Those are the only graphs that can appear in a forbidden subgraph characterization for the hereditary property of having a price of connectivity at most t. In particular, we completely characterize the critical graphs that are also chordal. Finally, we also consider the question of computing the price of connectivity of a given graph. Unsurprisingly, the decision version of this question is NP-hard. In fact, we show that it is even complete for the class Θ₂^P = P^NP[\log], the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle. This paves the way for a thorough investigation of the complexity of problems involving ratios of graph invariants.
On the Meyniel condition for hamiltonicity in bipartite digraphs
Authors: Adamus Janusz , Adamus Lech , Yeo Anders
Published: August 2021

Graph Theory

We prove a sharp Meyniel-type criterion for hamiltonicity of a balanced bipartite digraph: For a≥2, a strongly connected balanced bipartite digraph D on 2a vertices is hamiltonian if d(u)+d(v)≥3a whenever uv∉A(D) and vu∉A(D). As a consequence, we obtain a sharp sufficient condition for hamiltonicity in terms of the minimal degree: a strongly connected balanced bipartite digraph D on 2a vertices is hamiltonian if δ(D)≥3a/2.
Sequential selection of the k best out of nrankable objects
Authors: Bruss F. Thomas , Louchard Guy
Published: August 2021

The objective of this paper is to find in a setting of n sequential observations of objects a good online policy to select the k bestof these n uniquely rankable objects. This focus is motivated by the fact that it is hard to find closed form solutions of optimalstrategies for general k and n. Selection is without recall, and the idea is to investigate threshold functions which maintain allpresent information, that is thresholds which are functions of all selections made so far. Our main interest lies in the asymptoticbehaviour of these thresholds as n -> infinity and in the corresponding asymptotic performance of the threshold algorithm.
Influence of the tie-break rule on the end-vertex problem
Authors: Charbit Pierre , Habib Michel , Mamcarz Antoine
Published: August 2021

End-vertices of a given graph search may have some nice properties, as for example it is well known that the last vertex of Lexicographic Breadth First Search (LBFS) in a chordal graph is simplicial, see Rose, Tarjan and Lueker 1976. Therefore it is interesting to consider if these vertices can be recognized in polynomial time or not, as first studied in Corneil, Köhler and Lanlignel 2010. A graph search is a mechanism for systematically visiting the vertices of a graph. At each step of a graph search, the key point is the choice of the next vertex to be explored. Graph searches only differ by this selection mechanism during which a tie-break rule is used. In this paper we study how the choice of the tie-break in case of equality during the search, for a given graph search including the classic ones such as BFS and DFS, can determine the complexity of the end-vertex problem. In particular we prove a counterintuitive NP-completeness result for Breadth First Search solving a problem raised in Corneil, Köhler and Lanlignel 2010.
On the number of regular edge labelings
Authors: Buchin Kevin , Speckmann Bettina , Verdonschot Sander
Published: August 2021

Combinatorics

We prove that any irreducible triangulation on n vertices has O(4.6807n) regular edge labelings and that there are irreducible triangulations on n vertices with Ω(3.0426n) regular edge labelings. Our upper bound relies on a novel application of Shearer's entropy lemma. As an example of the wider applicability of this technique, we also improve the upper bound on the number of 2-orientations of a quadrangulation to O(1.87n).
An algorithmic analysis of Flood-It and Free-Flood-It on graph powers
Authors: Souza Uéverton dos Santos , Protti Fábio , Silva Maise
Published: August 2021

Analysis of Algorithms

Flood-it is a combinatorial game played on a colored graph G whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively to a fixed pivot. Free-Flood-it is a variant where the pivot can be freely chosen for each move of the game. The standard versions of Flood-it and Free-Flood-it are played on m ×n grids. In this paper we analyze the behavior of these games when played on other classes of graphs, such as d-boards, powers of cycles and circular grids. We describe polynomial time algorithms to play Flood-it on C2n (the second power of a cycle on n vertices), 2 ×n circular grids, and some types of d-boards (grids with a monochromatic column). We also show that Free-Flood-it is NP-hard on C2n and 2 ×n circular grids.
Bounding the monomial index and (1,l)-weight choosability of a graph
Authors: Seamone Ben
Published: August 2021

Graph Theory

Let G = (V,E) be a graph. For each e ∈E(G) and v ∈V(G), let Le and Lv, respectively, be a list of real numbers. Let w be a function on V(G) ∪E(G) such that w(e) ∈Le for each e ∈E(G) and w(v) ∈Lv for each v ∈V(G), and let cw be the vertex colouring obtained by cw(v) = w(v) + ∑ₑ ∋vw(e). A graph is (k,l)-weight choosable if there exists a weighting function w for which cw is proper whenever |Lv| ≥k and |Le| ≥l for every v ∈V(G) and e ∈E(G). A sufficient condition for a graph to be (1,l)-weight choosable was developed by Bartnicki, Grytczuk and Niwczyk (2009), based on the Combinatorial Nullstellensatz, a parameter which they call the monomial index of a graph, and matrix permanents. This paper extends their method to establish the first general upper bound on the monomial index of a graph, and thus to obtain an upper bound on l for which every admissible graph is (1,l)-weight choosable. Let ∂2(G) denote the smallest value s such that every induced subgraph of G has vertices at distance 2 whose degrees sum to at most s. We show that every admissible graph has monomial index at most ∂2(G) and hence that such graphs are (1, ∂2(G)+1)-weight choosable. While this does not improve the best known result on (1,l)-weight choosability, we show that the results can be extended to obtain improved bounds for some graph products; for instance, it is shown that G □ Kn is (1, nd+3)-weight choosable if G is d-degenerate.
Graphs with large disjunctive total domination number
Authors: Henning Michael A. , Naicker Viroshan
Published: August 2021

Graph Theory

Let G be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, γt(G). A set S of vertices in G is a disjunctive total dominating set of G if every vertex is adjacent to a vertex of S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number, γdt(G), is the minimum cardinality of such a set. We observe that γdt(G) ≤γt(G). Let G be a connected graph on n vertices with minimum degree δ. It is known [J. Graph Theory 35 (2000), 21 13;45] that if δ≥2 and n ≥11, then γt(G) ≤4n/7. Further [J. Graph Theory 46 (2004), 207 13;210] if δ≥3, then γt(G) ≤n/2. We prove that if δ≥2 and n ≥8, then γdt(G) ≤n/2 and we characterize the extremal graphs.
Extending a perfect matching to a Hamiltonian cycle
Authors: Alahmadi Adel , Aldred Robert E. L. , Alkenani Ahmad , Hijazi Rola , Solé P. , Thomassen Carsten
Published: August 2021

Graph Theory

Ruskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for every perfect matching M, remarkably even if M contains external edges. We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d ≥7 and every k, where 7 ≤k ≤d, the d-dimensional hypercube contains a k-regular spanning subgraph such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle. We do not know if this result can be extended to k=4,5,6. It cannot be extended to k=3. Indeed, there are only three 3-regular graphs such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle, namely the complete graph on 4 vertices, the complete bipartite 3-regular graph on 6 vertices and the 3-cube on 8 vertices. Also, we do not know if there are graphs of girth at least 5 with this matching-extendability property.
An efficient certificateless aggregate signature scheme for vehicular ad-hoc networks
Authors: Malhi Avleen Kaur , Batra Shalini
Published: August 2021

Distributed Computing and Networking

The state-of-the-art telecommunication technologies have widely been adapted for sensing the traffic related information and collection of it. Vehicular Ad-Hoc Networks (VANETs) have emerged as a novel technology for revolutionizing the driving experiences of human. The most effective and widely recognized way for mutual authentication among entities in VANETs is digital signature scheme. The new and attractive paradigm which eliminates the use of certificates in public key cryptography and solves the key escrow problem in identity based cryptography is certificateless cryptography. A new certificateless aggregate signature scheme is proposed in the paper for VANETs with constant pairing computations. Assuming the hardness of computational Diffie-Hellman Problem, the scheme is proved to be existentially unforgeable in the random oracle model against adaptive chosen-message attacks.
The complexity of deciding whether a graph admits an orientation with fixed weak diameter
Authors: Bensmail Julien , Duvignau Romaric , Kirgizov Sergey
Published: August 2021

An oriented graph $\overrightarrow{G}$ is said weak (resp. strong) if, for every pair $\{ u,v \}$ of vertices of $\overrightarrow{G}$, there are directed paths joining $u$ and $v$ in either direction (resp. both directions). In case, for every pair of vertices, some of these directed paths have length at most $k$, we call $\overrightarrow{G}$ $k$-weak (resp. $k$-strong). We consider several problems asking whether an undirected graph $G$ admits orientations satisfying some connectivity and distance properties. As a main result, we show that deciding whether $G$ admits a $k$-weak orientation is NP-complete for every $k \geq 2$. This notably implies the NP-completeness of several problems asking whether $G$ is an extremal graph (in terms of needed colours) for some vertex-colouring problems.
Permutations of context-free, ET0L and indexed languages
Authors: Brough Tara , Ciobanu Laura , Elder Murray , Zetzsche Georg
Published: August 2021

For a language $L$, we consider its cyclic closure, and more generally the language $C^{k}(L)$, which consists of all words obtained by partitioning words from $L$ into $k$ factors and permuting them. We prove that the classes of ET0L and EDT0L languages are closed under the operators $C^k$. This both sharpens and generalises Brandstädt's result that if $L$ is context-free then $C^{k}(L)$ is context-sensitive and not context-free in general for $k \geq 3$. We also show that the cyclic closure of an indexed language is indexed.
Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis
Authors: Thiéry Nicolas
Published: August 2021

We present a characteristic-free algorithm for computing minimal generating sets of invariant rings of permutation groups. We circumvent the main weaknesses of the usual approaches (using classical Gröbner basis inside the full polynomial ring, or pure linear algebra inside the invariant ring) by relying on the theory of SAGBI- Gröbner basis. This theory takes, in this special case, a strongly combinatorial flavor, which makes it particularly effective. Our algorithm does not require the computation of a Hironaka decomposition, nor even the computation of a system of parameters, and could be parallelized. Our implementation, as part of the library $permuvar$ for $mupad$, is in many cases much more efficient than the other existing software.
The Many Faces of Alternating-Sign Matrices
Authors: Propp James
Published: August 2021

I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three-colorings, monotone triangles, tetrahedral order ideals, square ice, gasket-and-basket tilings and full packings of loops.
A Bijection for Directed-Convex Polyominoes
Authors: Del Lungo Alberto , Mirolli Massimo , Pinzani Renzo , Rinaldi Simone
Published: August 2021

In this paper we consider two classes of lattice paths on the plane which use \textitnorth, \textiteast, \textitsouth,and \textitwest unitary steps, beginningand ending at (0,0).We enumerate them according to the number ofsteps by means of bijective arguments; in particular, we apply the cycle lemma.Then, using these results, we provide a bijective proof for the number of directed-convex polyominoes having a fixed number of rows and columns.
Results and conjectures on the Sandpile Identity on a lattice
Authors: Dartois Arnaud , Magnien Clémence
Published: August 2021

In this paper we study the identity of the Abelian Sandpile Model on a rectangular lattice.This configuration can be computed with the burning algorithm, which, starting from the empty lattice, computes a sequence of configurations, the last of which is the identity.We extend this algorithm to an infinite lattice, which allows us to prove that the first steps of the algorithm on a finite lattice are the same whatever its size.Finally we introduce a new configuration, which shares the intriguing properties of the identity, but is easier to study.
Noncommutative symmetric functions III : Deformations of Cauchy and convolution algebras
Authors: Duchamp Gérard , Klyachko Alexander , Krob Daniel , Thibon Jean-Yves
Published: August 2021

[in "Special Issue : Lie Computations", G. Jacob, V. Koseleff, Eds.]

This paper discusses various deformations of free associative algebras and of their convolution algebras. Our main examples are deformations of noncommutative symmetric functions related to families of idempotents in descent algebras, and a simple q-analogue of the shuffle product, which has unexpected connections with quantum groups, hyperplane arrangements, and certain questions in mathematical physics (the quon algebra, generalized Brownian motion).
Kazhdan-Lusztig polynomials of boolean elements
Authors: Mongelli Pietro
Published: August 2021

We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type $q$ in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J. Algebra 295 (2006)], in Coxeter groups whose Coxeter graph is a tree. Such formulas involve Catalan numbers and use a combinatorial interpretation of the Coxeter graph of the group. In the case of classical Weyl groups, this combinatorial interpretation can be restated in terms of statistics of (signed) permutations. As an application of the formulas, we compute the intersection homology Poincaré polynomials of the Schubert varieties of boolean elements.

Nous donnons des formules combinatoires pour les polynômes de Kazhdan-Lusztig et leurs analogues paraboliques de type $q$ pour les éléments booléens, introduite dans [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J. Algebra 295 (2006)], dans les groupes de Coxeter dont le graphe de Coxeter est un arbre. Ces formules utilisent les nombres de Catalan et une interprétation combinatoire des graphes du groupe de Coxeter. Dans le cas des groupes de Weyl classiques, cette interprétation combinatoire peut être reformulée en termes de statistiques de permutations avec signe. Avec ces formules, on peut calculer le polynôme de l’intersection homologie de Poincaré pour la variété de Schubert de éléments booléens.
Pattern-avoiding Dyck paths
Authors: Bernini Antonio , Ferrari Luca , Pinzani Renzo , West Julian
Published: August 2021

We introduce the notion of $\textit{pattern}$ in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the $\textit{Dyck pattern poset}$. Given a Dyck path $P$, we determine a formula for the number of Dyck paths covered by $P$, as well as for the number of Dyck paths covering $P$. We then address some typical pattern-avoidance issues, enumerating some classes of pattern-avoiding Dyck paths. Finally, we offer a conjecture concerning the asymptotic behavior of the sequence counting Dyck paths avoiding a generic pattern and we pose a series of open problems regarding the structure of the Dyck pattern poset.
The unreasonable ubiquitousness of quasi-polynomials
Authors: Woods Kevin
Published: August 2021

A function $g$, with domain the natural numbers, is a quasi-polynomial if there exists a period $m$ and polynomials $p_0,p_1,\ldots,p_m-1$ such that $g(t)=p_i(t)$ for $t\equiv i\bmod m$. Quasi-polynomials classically – and ``reasonably'' – appear in Ehrhart theory and in other contexts where one examines a family of polyhedra, parametrized by a variable t, and defined by linear inequalities of the form $a_1x_1+⋯+a_dx_d≤ b(t)$. Recent results of Chen, Li, Sam; Calegari, Walker; and Roune, Woods show a quasi-polynomial structure in several problems where the $a_i$ are also allowed to vary with $t$. We discuss these ``unreasonable'' results and conjecture a general class of sets that exhibit various (eventual) quasi-polynomial behaviors: sets $S_t$ that are defined with quantifiers $(\forall , ∃)$, boolean operations (and, or, not), and statements of the form $a_1(t)x_1+⋯+a_d(t)x_d ≤ b(t)$, where $a_i(t)$ and $b(t)$ are polynomials in $t$. These sets are a generalization of sets defined in the Presburger arithmetic. We prove several relationships between our conjectures, and we prove several special cases of the conjectures.
Some simple varieties of trees arising in permutation analysis
Authors: Bouvel Mathilde , Mishna Marni , Nicaud Cyril
Published: August 2021

After extending classical results on simple varieties of trees to trees counted by their number of leaves, we describe a filtration of the set of permutations based on their strong interval trees. For each subclass we provide asymptotic formulas for number of trees (by leaves), average number of nodes of fixed arity, average subtree size sum, and average number of internal nodes. The filtration is motivated by genome comparison of related species.

Nous commençons par étendre les résultats classiques sur les variétés simples d'arbres aux arbres comptés selon leur nombre de feuilles, puis nous décrivons une filtration de l'ensemble des permutations qui repose sur leurs arbres des intervalles communs. Pour toute sous-classe, nous donnons des formules asymptotiques pour le nombre d'arbres (comptés selon les feuilles), le nombre moyen de nœuds d'arité fixée, la moyenne de la somme des tailles des sous-arbres, et le nombre moyen de nœuds internes. Cette filtration est motivée par des problématiques de comparaison de génomes.
Counting strings over $\mathbb{Z}2^d$ with Given Elementary Symmetric Function Evaluations
Authors: Miers Charles Robert , Ruskey Franck
Published: August 2021

Let $\alpha$ be a string over $\mathbb{Z}_q$, where $q = 2^d$. The $j$-th elementary symmetric function evaluated at $\alpha$ is denoted $e_j(\alpha)$ . We study the cardinalities $S_q(m;\mathcal{T} _1,\mathcal{T} _2,\ldots,\mathcal{T} _t)$ of the set of length $m$ strings for which $e_j(\alpha) = \tau _i$. The $\textit{profile}$ k$(\alpha) = ⟨k_1,k_2,\ldots,k_(q-1) ⟩$ of a string $\alpha$ is the sequence of frequencies with which each letter occurs. The profile of $\alpha$ determines $e_j(\alpha)$ , and hence $S_q$. Let $h_n$ : $\mathbb{Z}_{2^{n+d-1}}^{(q-1)}$ $\mapsto \mathbb{Z}_{2^d} [z] $ mod $ z^{2^n}$ be the map that takes k$(\alpha)$ mod $2^{n+d-1}$ to the polynomial $1+ e_1(\alpha) z + e_2(\alpha) z^2 + ⋯+ e_{2^n-1}(\alpha)$ $z^{2^{n-1}}$. We show that $h_n$ is a group homomorphism and establish necessary conditions for membership in the kernel for fixed $d$. The kernel is determined for $d$ = 2,3. The range of $h_n$ is described for $d$ = 2. These results are used to efficiently compute $S_4(m;\mathcal{T} _1,\mathcal{T} _2,\ldots,\mathcal{T} _t)$ for $d$ = 2 and the number of complete factorizations of certain polynomials.
Long Cycle Factorizations: Bijective Computation in the General Case
Authors: Vassilieva Ekaterina A.
Published: August 2021

This paper is devoted to the computation of the number of ordered factorizations of a long cycle in the symmetric group where the number of factors is arbitrary and the cycle structure of the factors is given. Jackson (1988) derived the first closed form expression for the generating series of these numbers using the theory of the irreducible characters of the symmetric group. Thanks to a direct bijection we compute a similar formula and provide the first purely combinatorial evaluation of these generating series.

Cet article est dédié au calcul du nombre de factorisations d’un long cycle du groupe symétrique pour lesquels le nombre de facteurs est arbitraire et la structure des cycles des facteurs est donnée. Jackson (1988) a dérivé la première expression compacte pour les séries génératrices de ces nombres en utilisant la théorie des caractères irréductibles du groupe symétrique. Grâce à une bijection directe nous démontrons une formule similaire et donnons ainsi la première évaluation purement combinatoire de ces séries génératrices.
A direct bijective proof of the hook-length formula
Authors: Novelli Jean-Christophe , Pak Igor , Stoyanovskii Alexander V.
Published: August 2021

This paper presents a new proof of the hook-length formula, which computes the number of standard Young tableaux of a given shape. After recalling the basic definitions, we present two inverse algorithms giving the desired bijection. The next part of the paper presents the proof of the bijectivity of our construction. The paper concludes with some examples.
Two bijections on Tamari Intervals
Authors: Chapoton Frédéric , Chatel Gregory , Pons Viviane
Published: August 2021

We use a recently introduced combinatorial object, the $\textit{interval-poset}$, to describe two bijections on intervals of the Tamari lattice. Both bijections give a combinatorial proof of some previously known results. The first one is an inner bijection between Tamari intervals that exchanges the $\textit{initial rise}$ and $\textit{lower contacts}$ statistics. Those were introduced by Bousquet-Mélou, Fusy, and Préville-Ratelle who proved they were symmetrically distributed but had no combinatorial explanation. The second bijection sends a Tamari interval to a closed flow of an ordered forest. These combinatorial objects were studied by Chapoton in the context of the Pre-Lie operad and the connection with the Tamari order was still unclear.

Nous utilisons les $\textit{intervalles-posets}$, très récemment introduits, pour décrire deux bijections sur les intervalles du treillis de Tamari. Nous obtenons ainsi des preuves combinatoires de précédents résultats. La première bijection est une opération interne sur les intervalles qui échange les statistiques de la $\textit{montée initiale}$ et du $\textit{nombre de contacts}$. Ces dernières ont été introduites par Bousquet-Mélou, Fusy et Préville-Ratelle qui ont prouvé qu’elles étaient symétriquement distribuées sans pour autant proposer d’explication combinatoire. La seconde bijection fait le lien avec un objet étudié par Chapoton dans le cadre de l’opérade Pré-Lie : les flots sur les forêts ordonnées. Le lien avec l’ordre de Tamari avait déjà été remarqué sans pour autant être expliqué.
Estimating deep Littlewood-Richardson Coefficients
Authors: Narayanan Hariharan
Published: August 2021

Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups $(GL_n)$. The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for Littlewood-Richardson coefficients corresponding to indices sufficiently far from the boundary of the Littlewood Richardson cone. 2. A proof of approximate log-concavity of the above mentioned class of Littlewood-Richardson coefficients.

Coefficients de Littlewood Richardson sont des constantes de structure apparaissant dans la théorie de la représentation des groupes linéaires généraux $(GL_n)$. Les principaux résultats de cette étude sont les suivants: 1. Un schéma d’approximation polynomiale randomisée fortement pour des coefficients de Littlewood-Richardson correspondant aux indices suffisamment loin de la limite du cône Littlewood Richardson. 2. Une preuve de l’approximatif log-concavité de la classe de coefficients de Littlewood-Richardson mentionné ci-dessus.
Descents of $\lambda$-unimodal cyclic permutations
Authors: Archer Kassie
Published: August 2021

We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.

Nous prouvons une identité conjecturée par Adin et Roichman impliquant les ensembles des descentes des permutations cycliques $\lambda$-unimodales. Ces permutations apparaissent dans les formules des caractères pour certaines représentations du groupe symétrique, et ces formules sont généralement prouvées dans une manière algébrique. Ici, nous donnons une preuve combinatoire pour une telle formule et discutons les conséquences pour la distribution de l’ensemble des descentes sur des permutations cycliques.
Bijections on m-level Rook Placements
Authors: Barrese Kenneth , Sagan Bruce
Published: August 2021

Partition the rows of a board into sets of $m$ rows called levels. An $m$-level rook placement is a subset of squares of the board with no two in the same column or the same level. We construct explicit bijections to prove three theorems about such placements. We start with two bijections between Ferrers boards having the same number of $m$-level rook placements. The first generalizes a map by Foata and Schützenberger and our proof applies to any Ferrers board. The second generalizes work of Loehr and Remmel. This construction only works for a special class of Ferrers boards but also yields a formula for calculating the rook numbers of these boards in terms of elementary symmetric functions. Finally we generalize another result of Loehr and Remmel giving a bijection between boards with the same hit numbers. The second and third bijections involve the Involution Principle of Garsia and Milne.

Nous considérons les rangs d’un échiquier partagés en ensembles de $m$ rangs appelés les niveaux. Un $m$-placement des tours est un sous-ensemble des carrés du plateau tel qu’il n’y a pas deux carrés dans la même colonne ou dans le même niveau. Nous construisons deux bijections explicites entre des plateaux de Ferrers ayant les mêmes nombres de $m$-placements. La première est une généralisation d’une fonction de Foata et Schützenberger et notre démonstration est pour n’importe quels plateaux de Ferrers. La deuxième généralise une bijection de Loehr et Remmel. Cette construction marche seulement pour des plateaux particuliers, mais ça donne une formule pour le nombre de $m$-placements en terme des fonctions symétriques élémentaires. Enfin, nous généralisons un autre résultat de Loehr et Remmel donnant une bijection entre deux plateaux ayant les mêmes nombres de coups. Les deux dernières bijections utilisent le Principe des Involutions de Garsia et Milne.
Combinatorics of diagrams of permutations
Authors: Lewis Joel Brewster , Morales Alejandro
Published: August 2021

There are numerous combinatorial objects associated to a Grassmannian permutation $w_λ$ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and their q-analogues in the case of permutations $\mathcal{w}$ that are not necessarily Grassmannian.
Chevalley-Monk and Giambelli formulas for Peterson Varieties
Authors: Drellich Elizabeth
Published: August 2021

A Peterson variety is a subvariety of the flag variety $G/B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type A Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives a Chevalley-Monk rule and Giambelli's formula for all Lie types.
Honeycombs from Hermitian Matrix Pairs
Authors: Appleby Glenn , Whitehead Tamsen
Published: August 2021

Knutson and Tao's work on the Horn conjectures used combinatorial invariants called hives and honeycombs to relate spectra of sums of Hermitian matrices to Littlewood-Richardson coefficients and problems in representation theory, but these relationships remained implicit. Here, let $M$ and $N$ be two $n ×n$ Hermitian matrices. We will show how to determine a hive $\mathcal{H}(M, N)={H_ijk}$ using linear algebra constructions from this matrix pair. With this construction, one may also define an explicit Littlewood-Richardson filling (enumerated by the Littlewood-Richardson coefficient $c_μν ^λ$ associated to the matrix pair). We then relate rotations of orthonormal bases of eigenvectors of $M$ and $N$ to deformations of honeycombs (and hives), which we interpret in terms of the structure of crystal graphs and Littelmann's path operators. We find that the crystal structure is determined \emphmore simply from the perspective of rotations than that of path operators.
Some combinatorial identities involving noncommuting variables
Authors: Schlosser Michael , Yoo Meesue
Published: August 2021

We derive combinatorial identities for variables satisfying specific sets of commutation relations. The identities thus obtained extend corresponding ones for $q$-commuting variables $x$ and $y$ satisfying $yx=qxy$. In particular, we obtain weight-dependent binomial theorems, functional equations for generalized exponential functions, we propose a derivative of noncommuting variables, and finally utilize one of the considered weight functions to extend rook theory. This leads us to an extension of the $q$-Stirling numbers of the second kind, and of the $q$-Lah numbers.

Nous obtenons des identités combinatoires pour des variables satisfaisant des ensembles spécifiques de relations de commutation. Ces identités ainsi obtenues généralisent leurs analogues pour des variables $q$-commutantes $x$ et $y$ satisfaisant $yx=qxy$. En particulier, nous obtenons des théorèmes binomiaux dépendant du poids, des équations fonctionnelles pour les fonctions exponentielles généralisées, nous proposons une dérivée des variables non-commutatives, et finalement nous utilisons l’une des fonctions de poids considérées pour étendre la théorie des tours. Nous en déduisons une généralisation des $q$-nombres de Stirling de seconde espèce et des $q$-nombres de Lah.
A Categorification of One-Variable Polynomials
Authors: Khovanov Mikhail , Sazdanovic Radmila
Published: August 2021

We develop a diagrammatic categorification of the polynomial ring $\mathbb{Z} [x]$, based on a geometrically-defined graded algebra and show how to lift various operations on polynomials to the categorified setting. Our categorification satisfies a version of the Bernstein-Gelfand-Gelfand reciprocity property, with indecomposable projective modules corresponding to $x^n$ and standard modules to $(x -1)^n$ in the Grothendieck ring. This construction generalizes tocategorification of various orthogonal polynomials.

Résumé. Catégorification de l’anneau des polynômes $\mathbb{Z} [x]$, Nous développons une catégorification diagrammatique de l’anneau des polynômes $\mathbb{Z} [x]$, s’appuyant sur une algèbre graduée définie de manière géométrique, et nous décrivons comment on peut relever certaines opérations sur les polynômes dans cette catégorification. Notre catégorification vérifie une version de la réciprocité de Bernstein-Gelfand-Gelfand, avec les modules projectifs indécomposables correspondants à $x^n$ et les modules standards correspondants à $(x - 1)^n$ dans l’anneau de Grothendieck. Cette construction se généralise à certains polynômes orthogonaux.
The polytope of Tesler matrices
Authors: Mészáros Karola , Morales Alejandro H. , Rhoades Brendon
Published: August 2021

26 pages, 4 figures. v2 has typos fixed, updated references, and a final remarks section including remarks from previous sections

We introduce the Tesler polytope $Tes_n(a)$, whose integer points are the Tesler matrices of size n with hook sums $a_1,a_2,...,a_n in Z_{\geq 0}$. We show that $Tes_n(a)$ is a flow polytope and therefore the number of Tesler matrices is counted by the type $A_n$ Kostant partition function evaluated at $(a_1,a_2,...,a_n,-\sum_{i=1}^n a_i)$. We describe the faces of this polytope in terms of "Tesler tableaux" and characterize when the polytope is simple. We prove that the h-vector of $Tes_n(a)$ when all $a_i>0$ is given by the Mahonian numbers and calculate the volume of $Tes_n(1,1,...,1)$ to be a product of consecutive Catalan numbers multiplied by the number of standard Young tableaux of staircase shape.

On présente le polytope de Tesler $Tes_n(a)$, dont les points réticuilaires sont les matrices de Tesler de taillen avec des sommes des équerres $a_1,a_2,...,a_n in Z_{\geq 0}$. On montre que $Tes_n(a)$ est un polytope de flux. Donc lenombre de matrices de Tesler est donné par la fonction de Kostant de type An évaluée à ($(a_1,a_2,...,a_n,-\sum_{i=1}^n a_i)$On décrit les faces de ce polytope en termes de “tableaux de Tesler” et on caractérise quand le polytope est simple.On montre que l’h-vecteur de $Tes_n(a)$ , quand tous les $a_i>0$ , est donnée par le nombre de permutations avec unnombre donné d’inversions et on calcule le volume de T$Tes_n(1,1,...,1)$ comme un produit de nombres de Catalanconsécutives multiplié par le nombre de tableaux standard de Young en forme d’escalier
Genomic Tableaux and Combinatorial $K$-Theory
Authors: Pechenik Oliver , Yong Alexander
Published: August 2021

We introduce genomic tableaux, with applications to Schubert calculus. We report a combinatorial rule for structure coefficients in the torus-equivariant $K$-theory of Grassmannians for the basis of Schubert structure sheaves. This rule is positive in the sense of [Anderson-Griffeth-Miller ’11]. We thereby deduce an earlier conjecture of [Thomas-Yong ’13] for the coefficients. Moreover, our rule specializes to give a new Schubert calculus rule in the (non-equivariant) $K$-theory of Grassmannians. From this perspective, we also obtain a new rule for $K$-theoretic Schubert structure constants of maximal orthogonal Grassmannians, and give conjectural bounds on such constants for Lagrangian Grassmannians.

Nous introduisons la notion de tableau génomique, pour l’appliquer au calcul de Schubert. Nous énonçons une règle combinatoire pour les coefficients de structure de la $K$-théorie tore-équivariante des grassmanniennes, dans la base définie par les classes des faisceaux structuraux des variétés de Schubert. Cette règle est positive au sens de [Anderson-Griffeth-Miller ’11]. Nous en déduisons une conjecture de [Thomas-Yong ’13]. De plus, notre règle se spécialise en une règle nouvelle pour le calcul de Schubert dans la $K$-théorie (non équivariante) des grassmanniennes. Nous obtenons également une nouvelle règle pour les coefficients de structure de la $K$-théorie des grassmanniennes orthogonales maximales dans la base de Schubert, et nous conjecturons certaines bornes pour ces coefficients dans le cas des grassmanniennes lagrangiennes.
The freeness of Ish arrangements
Authors: Abe Takuro , Suyama Daisuke , Tsujie Shuhei
Published: August 2021

The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement and posed some problems. One of them is whether the Ish arrangement is a free arrangement or not. In this paper, we verify that the Ish arrangement is supersolvable and hence free. Moreover, we give a necessary and sufficient condition for the deleted Ish arrangement to be free

L’arrangement Ish a été introduit par Armstrong pour donner une nouvelle interprétation des nombres $q; t$-Catalan de Garsia et Haiman. Armstrong et Rhoades ont montré qu’il y avait des ressemblances frappantes entre l’arrangement Shi et l’arrangement Ish et ont posé des conjectures. L’une d’elles est de savoir si l’arrangement Ish est un arrangement libre ou pas. Dans cet article, nous vérifions que l’arrangement Ish est supersoluble et donc libre. De plus, on donne une condition nécessaire et suffisante pour que l’arrangement Ish réduit soit libre.