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rEulerMahonian statistics on permutations J. Comb. Theory A (IF 0.9) Pub Date : 20240806
ShaoHua LiuLet and denote the permutation statistics descent number and excedance number, respectively. We prove that the pairs of permutation statistics and are equidistributed, where denotes the major index defined by Don Rawlings and denotes the Denert's statistic defined by GuoNiu Han. When , this result reduces to the equidistribution of and , which was conjectured by Denert in 1990 and proved that

The qOnsager algebra and the quantum torus J. Comb. Theory A (IF 0.9) Pub Date : 20240802
Owen GoffThe Onsager algebra, denoted , is defined by two generators and two relations called the DolanGrady relations. Recently, Terwilliger introduced some elements of , said to be alternating. These elements are denoted

An infinite family of hyperovals of Q+(5,q), q even J. Comb. Theory A (IF 0.9) Pub Date : 20240801
Bart De BruynWe construct an infinite family of hyperovals on the Klein quadric , even. The construction makes use of ovoids of the symplectic generalized quadrangle that is associated with an elliptic quadric which arises as solid intersection with . We also solve the isomorphism problem: we determine necessary and sufficient conditions for two hyperovals arising from the construction to be isomorphic.

A proof of the EtzionSilberstein conjecture for monotone and MDSconstructible Ferrers diagrams J. Comb. Theory A (IF 0.9) Pub Date : 20240724
Alessandro Neri, Mima StanojkovskiFerrers diagram rankmetric codes were introduced by Etzion and Silberstein in 2009. In their work, they proposed a conjecture on the largest dimension of a space of matrices over a finite field whose nonzero elements are supported on a given Ferrers diagram and all have rank lower bounded by a fixed positive integer . Since stated, the EtzionSilberstein conjecture has been verified in a number of

New string attractorbased complexities for infinite words J. Comb. Theory A (IF 0.9) Pub Date : 20240718
Julien Cassaigne, France Gheeraert, Antonio Restivo, Giuseppe Romana, Marinella Sciortino, Manon StipulantiA is a set of positions in a word such that each distinct factor has an occurrence crossing a position from the set. This definition comes from the data compression field, where the size of a smallest string attractor represents a lower bound for the output size of a large family of string compressors exploiting repetitions in words, including BWTbased and LZbased compressors. For finite words, the

Cluster braid groups of CoxeterDynkin diagrams J. Comb. Theory A (IF 0.9) Pub Date : 20240710
Zhe Han, Ping He, Yu QiuCluster exchange groupoids are introduced by KingQiu as an enhancement of cluster exchange graphs to study stability conditions and quadratic differentials. In this paper, we introduce the cluster exchange groupoid for any finite CoxeterDynkin diagram Δ and show that its fundamental group is isomorphic to the corresponding braid group associated with Δ.

Restricted bargraphs and unimodal compositions J. Comb. Theory A (IF 0.9) Pub Date : 20240705
Rigoberto Flórez, José L. Ramírez, Diego VillamizarIn this paper, we present a study on , which are polygons created by connecting unit squares along their edges. Specifically, we focus on a related concept called a , which is a path on a lattice in traced along the boundaries of a column convex polyomino where the lower edge is on the axis. To explore new variations of bargraphs, we introduce the notion of , which incorporate an additional restriction

Positivity and tails of pentagonal number series J. Comb. Theory A (IF 0.9) Pub Date : 20240704
Nian Hong ZhouIn this paper, we refine a result of Andrews and Merca on truncated pentagonal number series. Subsequently, we establish some positivity results involving Andrews–Gordon–Bressoud identities and regular partitions. In particular, we prove several conjectures of Merca and Krattenthaler–Merca–Radu on truncated pentagonal number series.

On the difference of the enhanced power graph and the power graph of a finite group J. Comb. Theory A (IF 0.9) Pub Date : 20240621
Sucharita Biswas, Peter J. Cameron, Angsuman Das, Hiranya Kishore DeyThe difference graph of a finite group is the difference of the enhanced power graph of and the power graph of , where all isolated vertices are removed. In this paper we study the connectedness and perfectness of with respect to various properties of the underlying group . We also find several connections between the difference graph of and the GruenbergKegel graph of . We also examine the operation

Flagtransitive automorphism groups of 2designs with λ ≥ (r,λ)2 are not product type J. Comb. Theory A (IF 0.9) Pub Date : 20240619
Huiling Li, Zhilin Zhang, Shenglin ZhouIn this note we show that a flagtransitive automorphism group of a nontrivial 2 design with is not of product action type. In conclusion, is a primitive group of affine or almost simple type.

Intersection density of imprimitive groups of degree pq J. Comb. Theory A (IF 0.9) Pub Date : 20240612
Angelot Behajaina, Roghayeh Maleki, Andriaherimanana Sarobidy RazafimahatratraA subset of a finite transitive group is if any two elements of agree on an element of Ω. The of is the number where and is the stabilizer of in . It is known that if is an imprimitive group of degree a product of two odd primes admitting a block of size or two complete block systems, whose blocks are of size , then .

Birational geometry of generalized Hessenberg varieties and the generalized ShareshianWachs conjecture J. Comb. Theory A (IF 0.9) Pub Date : 20240304
YoungHoon Kiem, Donggun LeeWe introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group on the cohomology of Hessenberg varieties extends to generalized Hessenberg varieties and that natural morphisms among them preserve the action. By analyzing natural morphisms and birational maps among generalized Hessenberg varieties, we give an elementary proof of the ShareshianWachs

The second largest eigenvalue of normal Cayley graphs on symmetric groups generated by cycles J. Comb. Theory A (IF 0.9) Pub Date : 20240301
Yuxuan Li, Binzhou Xia, Sanming ZhouWe study the normal Cayley graphs on the symmetric group , where and is the set of all cycles in with length in . We prove that the strictly second largest eigenvalue of can only be achieved by at most four irreducible representations of , and we determine further the multiplicity of this eigenvalue in several special cases. As a corollary, in the case when contains neither nor we know exactly when

A short combinatorial proof of dimension identities of Erickson and Hunziker J. Comb. Theory A (IF 0.9) Pub Date : 20240229
Nishu KumariIn a recent paper (), Erickson and Hunziker consider partitions in which the arm–leg difference is an arbitrary constant . In previous works, these partitions are called asymmetric partitions. Regarding these partitions and their conjugates as highest weights, they prove an identity yielding an infinite family of dimension equalities between and modules. Their proof proceeds by the manipulations of

On the deepest cycle of a random mapping J. Comb. Theory A (IF 0.9) Pub Date : 20240222
Ljuben Mutafchiev, Steven FinchLet be the set of all mappings . The corresponding graph of is a union of disjoint connected unicyclic components. We assume that each is chosen uniformly at random (i.e., with probability ). The cycle of contained within its largest component is called the one. For any , let denote the length of this cycle. In this paper, we establish the convergence in distribution of and find the limits of its expectation

Two conjectures of Andrews, Merca and Yee on truncated theta series J. Comb. Theory A (IF 0.9) Pub Date : 20240222
Shane Chern, Ernest X.W. XiaIn their study of the truncation of Euler's pentagonal number theorem, Andrews and Merca introduced a partition function to count the number of partitions of in which is the least integer that is not a part and there are more parts exceeding than there are below . In recent years, two conjectures concerning on truncated theta series were posed by Andrews, Merca, and Yee. In this paper, we prove that

Constructing generalized Heffter arrays via near alternating sign matrices J. Comb. Theory A (IF 0.9) Pub Date : 20240221
L. Mella, T. Traetta 
On the maximal number of elements pairwise generating the finite alternating group J. Comb. Theory A (IF 0.9) Pub Date : 20240214
Francesco Fumagalli, Martino Garonzi, Pietro GheriLet be the alternating group of degree . Let be the maximal size of a subset of such that whenever and and let be the minimal size of a family of proper subgroups of whose union is . We prove that, when varies in the family of composite numbers, tends to 1 as . Moreover, we explicitly calculate for congruent to 3 modulo 18.


A Qpolynomial structure for the Attenuated Space poset Aq(N,M) J. Comb. Theory A (IF 0.9) Pub Date : 20240209
Paul TerwilligerThe goal of this article is to display a polynomial structure for the Attenuated Space poset . The poset is briefly described as follows. Start with an dimensional vector space over a finite field with elements. Fix an dimensional subspace of . The vertex set of consists of the subspaces of that have zero intersection with . The partial order on is the inclusion relation. The polynomial structure

Most plane curves over finite fields are not blocking J. Comb. Theory A (IF 0.9) Pub Date : 20240209
Shamil Asgarli, Dragos Ghioca, Chi Hoi YipA plane curve of degree is called if every line in the plane meets at some point. We prove that the proportion of blocking curves among those of degree is when and . We also show that the same conclusion holds for smooth curves under the somewhat weaker condition and . Moreover, the two events in which a random plane curve is smooth and respectively blocking are shown to be asymptotically independent

Spectral characterization of the complete graph removing a cycle J. Comb. Theory A (IF 0.9) Pub Date : 20240209
Muhuo Liu, Xiaofeng Gu, Haiying Shan, Zoran StanićA graph is determined by its spectrum if there is not another graph with the same spectrum. Cámara and Haemers proved that the graph , obtained from the complete graph with vertices by deleting all edges of a cycle with vertices, is determined by its spectrum for , but not for . In this paper, we show that is the unique exception for the spectral determination of .

The divisor class group of a discrete polymatroid J. Comb. Theory A (IF 0.9) Pub Date : 20240208
Jürgen Herzog, Takayuki Hibi, Somayeh Moradi, Ayesha Asloob QureshiIn this paper we introduce toric rings of multicomplexes. We show how to compute the divisor class group and the class of the canonical module when the toric ring is normal. In the special case that the multicomplex is a discrete polymatroid, its toric ring is studied deeply for several classes of polymatroids.

Large sumfree sets in Z5n J. Comb. Theory A (IF 0.9) Pub Date : 20240202
Vsevolod F. LevIt is wellknown that for a prime and integer , the maximum possible size of a sumfree subset of the elementary abelian group is . However, the matching stability result is known for only. We consider the first open case showing that if is a sumfree subset with , then there are a subgroup of size and an element such that .

Blocktransitive 2designs with a chain of imprimitive pointpartitions J. Comb. Theory A (IF 0.9) Pub Date : 20240201
Carmen Amarra, Alice Devillers, Cheryl E. PraegerMore than 30 years ago, Delandtsheer and Doyen showed that the automorphism group of a blocktransitive 2design, with blocks of size , could leave invariant a nontrivial pointpartition, but only if the number of points was bounded in terms of . Since then examples have been found where there are two nontrivial point partitions, either forming a chain of partitions, or forming a grid structure on

Large monochromatic components in colorings of complete hypergraphs J. Comb. Theory A (IF 0.9) Pub Date : 20240201
Lyuben Lichev, Sammy LuoGyárfás famously showed that in every rcoloring of the edges of the complete graph Kn, there is a monochromatic connected component with at least nr−1 vertices. A recent line of study by Conlon, Tyomkyn, and the second author addresses the analogous question about monochromatic connected components with many edges. In this paper, we study a generalization of these questions for kuniform hypergraphs

A study on free roots of BorcherdsKacMoody Lie superalgebras J. Comb. Theory A (IF 0.9) Pub Date : 20240125
Shushma Rani, G. ArunkumarConsider a BorcherdsKacMoody Lie superalgebra, denoted as g, associated with the graph G. This Lie superalgebra is constructed from a free Lie superalgebra by introducing three sets of relations on its generators: (1) Chevalley relations, (2) Serre relations, and (3) The commutation relations derived from the graph G. The Chevalley relations lead to a triangular decomposition of g as g=n+⊕h⊕n−, where

Further refinements of Wilfequivalence for patterns of length 4 J. Comb. Theory A (IF 0.9) Pub Date : 20240125
Robin D.P. Zhou, Yongchun Zang, Sherry H.F. YanIn this paper, we construct a bijection between 3142avoiding permutations and 3241avoiding permutations which proves the equidistribution of five classical setvalued statistics. Our bijection also enables us to establish a bijection between 3142avoiding permutations and 4132avoiding permutations, and a bijection between 2413avoiding permutations and 1423avoiding permutations, both of which preserve

New results on orthogonal arrays OA(3,5,4n + 2) J. Comb. Theory A (IF 0.9) Pub Date : 20240124
Dongliang Li, Haitao CaoAn orthogonal array of index unity, order v, degree 5 and strength 3, or an OA(3,5,v) in short, is a 5×v3 array on v symbols and in every 3×v3 subarray, each 3tuple column vector occurs exactly once. The existence of an OA(3,5,4n+2) is still open except for few known infinite classes of n. In this paper, we introduce a new combinatorial structure called three dimensions orthogonal complete large sets

qSupercongruences from Jackson's ϕ78 summation and Watson's ϕ78 transformation J. Comb. Theory A (IF 0.9) Pub Date : 20240112
Chuanan WeiqSupercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some qsupercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of Jackson's ϕ78 summation, Watson's ϕ78 transformation, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for


Nowherezero 3flows in Cayley graphs on supersolvable groups J. Comb. Theory A (IF 0.9) Pub Date : 20231228
Junyang Zhang, Sanming ZhouTutte's 3flow conjecture asserts that every 4edgeconnected graph admits a nowherezero 3flow. We prove that this conjecture is true for every Cayley graph of valency at least four on any supersolvable group with a noncyclic Sylow 2subgroup and every Cayley graph of valency at least four on any group whose derived subgroup is of squarefree order.

Algebraic approach to the completeness problem for (k,n)arcs in planes over finite fields J. Comb. Theory A (IF 0.9) Pub Date : 20231213
Gábor Korchmáros, Gábor P. Nagy, Tamás SzőnyiIn a projective plane over a finite field, complete (k,n)arcs with few characters are rare but interesting objects with several applications to finite geometry and coding theory. Since almost all known examples are large, the construction of small ones, with k close to the order of the plane, is considered a hard problem. A natural candidate to be a small (k,n)arc with few characters is the set Ω(C)

Neighbourtransitive codes in Kneser graphs J. Comb. Theory A (IF 0.9) Pub Date : 20231214
Dean Crnković, Daniel R. Hawtin, Nina Mostarac, Andrea ŠvobA code C is a subset of the vertex set of a graph and C is sneighbourtransitive if its automorphism group Aut(C) acts transitively on each of the first s+1 parts C0,C1,…,Cs of the distance partition {C=C0,C1,…,Cρ}, where ρ is the covering radius of C. While codes have traditionally been studied in the Hamming and Johnson graphs, we consider here codes in the Kneser graphs. Let Ω be the underlying

Chiral polytopes whose smallest regular cover is a polytope J. Comb. Theory A (IF 0.9) Pub Date : 20231208
Gabe CunninghamWe give a criterion for when the smallest regular cover of a chiral polytope P is itself a polytope, using only information about the facets and vertexfigures of P.

Asymptotics for real monotone double Hurwitz numbers J. Comb. Theory A (IF 0.9) Pub Date : 20231208
Yanqiao Ding, Qinhao HeIn recent years, monotone double Hurwitz numbers were introduced as a naturally combinatorial modification of double Hurwitz numbers. Monotone double Hurwitz numbers share many structural properties with their classical counterparts, such as piecewise polynomiality, while the quantitative properties of these two numbers are quite different. We consider real analogues of monotone double Hurwitz numbers

The method of constant terms and kcolored generalized Frobenius partitions J. Comb. Theory A (IF 0.9) Pub Date : 20231201
SuPing Cui, Nancy S.S. Gu, Dazhao TangIn his 1984 AMS memoir, Andrews introduced the family of kcolored generalized Frobenius partition functions. For any positive integer k, let cϕk(n) denote the number of kcolored generalized Frobenius partitions of n. Among many other things, Andrews proved that for any n≥0, cϕ2(5n+3)≡0(mod5). Since then, many scholars subsequently considered congruence properties of various kcolored generalized

Monochromatic arithmetic progressions in automatic sequences with group structure J. Comb. Theory A (IF 0.9) Pub Date : 20231201
Ibai Aedo, Uwe Grimm, Neil Mañibo, Yasushi Nagai, Petra StaynovaWe determine asymptotic growth rates for lengths of monochromatic arithmetic progressions in certain automatic sequences. In particular, we look at (onesided) fixed points of aperiodic, primitive, bijective substitutions and spin substitutions, which are generalisations of the Thue–Morse and Rudin–Shapiro substitutions, respectively. For such infinite words, we show that there exists a subsequence

The secondorder footballpool problem and the optimal rate of generalizedcovering codes J. Comb. Theory A (IF 0.9) Pub Date : 20231128
Dor Elimelech, Moshe SchwartzThe goal of the classic footballpool problem is to determine how many lottery tickets are to be bought in order to guarantee at least n−r correct guesses out of a sequence of n games played. We study a generalized (secondorder) version of this problem, in which any of these n games consists of two subgames. The secondorder version of the footballpool problem is formulated using the notion of

MacMahon's partition analysis XIV: Partitions with n copies of n J. Comb. Theory A (IF 0.9) Pub Date : 20231128
George E. Andrews, Peter PauleWe apply the methods of partition analysis to partitions with n copies of n. This allows us to obtain multivariable generating functions related to classical RogersRamanujan type identities. Also, partitions with n copies of n are extended to partition diamonds yielding numerous new results including a natural connection to overpartitions and a variety of partition congruences.

Singletontype bounds for listdecoding and listrecovery, and related results J. Comb. Theory A (IF 0.9) Pub Date : 20231128
Eitan Goldberg, Chong Shangguan, Itzhak TamoListdecoding and listrecovery are important generalizations of unique decoding and receive considerable attention over the years. We study the optimal tradeoff among the listdecoding (resp. listrecovery) radius, the list size, and the code rate, when the list size is constant and the alphabet size is large (both compared with the code length). We prove a new Singletontype bound for listdecoding

Matroid Horn functions J. Comb. Theory A (IF 0.9) Pub Date : 20231124
Kristóf Bérczi, Endre Boros, Kazuhisa MakinoHypergraph Horn functions were introduced as a subclass of Horn functions that can be represented by a collection of circular implication rules. These functions possess distinguished structural and computational properties. In particular, their characterizations in terms of implicateduality and the closure operator provide extensions of matroid duality and the Mac Lane – Steinitz exchange property

The Clebsch–Gordan coefficients of U(sl2) and the Terwilliger algebras of Johnson graphs J. Comb. Theory A (IF 0.9) Pub Date : 20231116
HauWen HuangThe universal enveloping algebra U(sl2) of sl2 is a unital associative algebra over C generated by E,F,H subject to the relations[H,E]=2E,[H,F]=−2F,[E,F]=H. The elementΛ=EF+FE+H22 is called the Casimir element of U(sl2). Let Δ:U(sl2)→U(sl2)⊗U(sl2) denote the comultiplication of U(sl2). The universal Hahn algebra H is a unital associative algebra over C generated by A,B,C and the relations assert that

Some refinements of Stanley's shuffle theorem J. Comb. Theory A (IF 0.9) Pub Date : 20231117
Kathy Q. Ji, Dax T.X. ZhangWe give a combinatorial proof of Stanley's shuffle theorem by using the insertion lemma of Haglund, Loehr and Remmel. Based on this combinatorial construction, we establish several refinements of Stanley's shuffle theorem.

A modular approach to AndrewsBeck partition statistics J. Comb. Theory A (IF 0.9) Pub Date : 20231115
Renrong MaoAndrews recently provided a qseries proof of congruences for NT(m,k,n), the total number of parts in the partitions of n with rank congruent to m modulo k. Motivated by Andrews' works, Chern obtain congruences for Mω(m,k,n) which denotes the total number of ones in the partition of n with crank congruent to m modulo k. In this paper, we focus on the modular approach to these new partition statistics

A bivariate Qpolynomial structure for the nonbinary Johnson scheme J. Comb. Theory A (IF 0.9) Pub Date : 20231024
Nicolas Crampé, Luc Vinet, Meri Zaimi, Xiaohong ZhangThe notion of multivariate P and Qpolynomial association scheme has been introduced recently, generalizing the wellknown univariate case. Numerous examples of such association schemes have already been exhibited. In particular, it has been demonstrated that the nonbinary Johnson scheme is a bivariate Ppolynomial association scheme. We show here that it is also a bivariate Qpolynomial association

Nonexpansive matrix number systems with bases similar to certain Jordan blocks J. Comb. Theory A (IF 0.9) Pub Date : 20231019
Joshua W. Caldwell, Kevin G. Hare, Tomáš VávraWe study representations of integral vectors in a number system with a matrix base M and vector digits. We focus on the case when M is equal or similar to Jn, the Jordan block with eigenvalue 1 and dimension n. If M=J2, we classify all digit sets of size two allowing representation for all of Z2. For M=Jn with n≥3, we show that a digit set of size three suffice to represent all of Zn. For bases M similar

On some double Nahm sums of Zagier J. Comb. Theory A (IF 0.9) Pub Date : 20231011
Zhineng Cao, Hjalmar Rosengren, Liuquan WangZagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no qseries proof for the tenth example. We prove that the fifth and the tenth examples are in fact equivalent. Then we give a qseries proof for the fifth example, which confirms a recent conjecture of Wang. This also serves as the first

Unionclosed sets and Horn Boolean functions J. Comb. Theory A (IF 0.9) Pub Date : 20231011
Vadim Lozin, Viktor ZamaraevA family F of sets is unionclosed if the union of any two sets from F belongs to F. The unionclosed sets conjecture states that if F is a finite unionclosed family of finite sets, then there is an element that belongs to at least half of the sets in F. The conjecture has several equivalent formulations in terms of other combinatorial structures such as lattices and graphs. In its whole generality

Partitioning into common independent sets via relaxing strongly base orderability J. Comb. Theory A (IF 0.9) Pub Date : 20230922
Kristóf Bérczi, Tamás SchwarczThe problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e. when the goal is to decide if two common independent sets suffice or not. Nevertheless, as the problem generalizes several longstanding open questions, identifying tractable cases is of particular interest. Strongly base orderable matroids

Twogeodesic transitive graphs of order pn with n ≤ 3 J. Comb. Theory A (IF 0.9) Pub Date : 20230918
JunJie Huang, YanQuan Feng, JinXin Zhou, FuGang YinA vertex triple (u,v,w) of a graph is called a 2geodesic if v is adjacent to both u and w and u is not adjacent to w. A graph is said to be 2geodesic transitive if its automorphism group is transitive on the set of 2geodesics. In this paper, a complete classification of 2geodesic transitive graphs of order pn is given for each prime p and n≤3. It turns out that all such graphs consist of three

A bijection for length5 patterns in permutations J. Comb. Theory A (IF 0.9) Pub Date : 20230918
Joanna N. Chen, Zhicong LinA bijection which preserves five classical setvalued permutation statistics between (31245,32145,31254,32154)avoiding permutations and (31425,32415,31524,32514)avoiding permutations is constructed. Combining this bijection with two codings of permutations introduced respectively by Baril–Vajnovszki and Martinez–Savage, we prove an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating

Trianguloids and triangulations of root polytopes J. Comb. Theory A (IF 0.9) Pub Date : 20230911
Pavel Galashin, Gleb Nenashev, Alexander PostnikovTriangulations of a product of two simplices and, more generally, of root polytopes are closely related to GelfandKapranovZelevinsky's theory of discriminants, to tropical geometry, tropical oriented matroids, and to generalized permutohedra. We introduce a new approach to these objects, identifying a triangulation of a root polytope with a certain bijection between lattice points of two generalized

Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs J. Comb. Theory A (IF 0.9) Pub Date : 20230908
Gary R.W. Greaves, Jeven SyatriadiWe show that the maximum cardinality of an equiangular line system in R18 is at most 59. Our proof includes a novel application of the Jacobi identity for complementary subgraphs. In particular, we show that there does not exist a graph whose adjacency matrix has characteristic polynomial (x−22)(x−2)42(x+6)15(x+8)2.

Singleton mesh patterns in multidimensional permutations J. Comb. Theory A (IF 0.9) Pub Date : 20230908
Sergey Avgustinovich, Sergey Kitaev, Jeffrey Liese, Vladimir Potapov, Anna TaranenkoThis paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional mesh patterns of length 1. A pattern is avoidable if there exist arbitrarily large permutations that do not contain it. As our main result, we give a complete characterization of avoidable SMPs using an invariant of a pattern

Improved ElekesSzabó type estimates using proximity J. Comb. Theory A (IF 0.9) Pub Date : 20230907
Jozsef Solymosi, Joshua ZahlWe prove a new ElekesSzabó type estimate on the size of the intersection of a Cartesian product A×B×C with an algebraic surface {f=0} over the reals. In particular, if A,B,C are sets of N real numbers and f is a trivariate polynomial, then either f has a special form that encodes additive group structure (for example, f(x,y,x)=x+y−z), or A×B×C∩{f=0} has cardinality O(N12/7). This is an improvement

Constructing uniform 2factorizations via rowsum matrices: Solutions to the HamiltonWaterloo problem J. Comb. Theory A (IF 0.9) Pub Date : 20230901
A.C. Burgess, P. Danziger, A. Pastine, T. TraettaIn this paper, we formally introduce the concept of a rowsum matrix over an arbitrary group G. When G is cyclic, these types of matrices have been widely used to build uniform 2factorizations of small Cayley graphs (or, Cayley subgraphs of blownup cycles), which themselves factorize complete (equipartite) graphs. Here, we construct rowsum matrices over a class of nonabelian groups, the generalized

Weighted Subspace Designs from qPolymatroids J. Comb. Theory A (IF 0.9) Pub Date : 20230822
Eimear Byrne, Michela Ceria, Sorina Ionica, Relinde JurriusThe AssmusMattson Theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs by Britz et al. in 2009. In this work we present a further twofold generalisation: first from matroids to polymatroids and also from sets to vector spaces. To achieve this, we study the characteristic polynomial of a qpolymatroid and outline several of its

On the polymatroid Tutte polynomial J. Comb. Theory A (IF 0.9) Pub Date : 20230816
Xiaxia Guan, Weiling Yang, Xian'an JinThe Tutte polynomial is a wellstudied invariant of matroids. The polymatroid Tutte polynomial TP(x,y), introduced by Bernardi, Kálmán, and Postnikov, is an extension of the classical Tutte polynomial from matroids to polymatroids P. In this paper, we first prove that TP(x,t) and TP(t,y) are interpolating for any fixed real number t≥1, and then we study the coefficients of highorder terms in TP(x

The full automorphism groups of general position graphs J. Comb. Theory A (IF 0.9) Pub Date : 20230814
Junyao PanLet S be a nonempty finite set. A flag of S is a set f of nonempty proper subsets of S such that X⊆Y or Y⊆X for all X,Y∈f. The set {X:X∈f} is called the type of f. Two flags f and f′ are in general position with respect to S if X∩Y=∅ or X∪Y=S for all X∈f and Y∈f′. For a fixed type T, Klaus Metsch defined the general position graph Γ(S,T) whose vertices are the flags of S of type T with two vertices