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The method of constant terms and kcolored generalized Frobenius partitions J. Comb. Theory A (IF 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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 1.1) 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

Proof of Dilks' bijectivity conjecture on Baxter permutations J. Comb. Theory A (IF 1.1) Pub Date : 20230807
Zhicong Lin, Jing LiuBaxter permutations originally arose in studying common fixed points of two commuting continuous functions. In 2015, Dilks proposed a conjectured bijection between Baxter permutations and nonintersecting triples of lattice paths in terms of inverse descent bottoms, descent positions and inverse descent tops. We prove this bijectivity conjecture by investigating its connection with the Françon–Viennot

Spinning switches on a wreath product J. Comb. Theory A (IF 1.1) Pub Date : 20230803
Peter KageyWe classify an algebraic phenomenon on several families of wreath products that can be seen as coming from a generalization of a puzzle about switches on the corners of a spinning table. Such puzzles have been written about and generalized since they were first popularized by Martin Gardner in 1979. In this paper, we build upon a paper of Bar Yehuda, Etzion, and Moran, a paper of Ehrenborg and Skinner

Hook length and symplectic content in partitions J. Comb. Theory A (IF 1.1) Pub Date : 20230731
T. Amdeberhan, G.E. Andrews, C. BallantineThe dimension of an irreducible representation of GL(n,C), Sp(2n), or SO(n) is given by the respective hook length and content formulas for the corresponding partition. The first author, inspired by the NekrasovOkounkov formula, conjectured combinatorial interpretations of analogous expressions involving hook lengths and symplectic/orthogonal contents. We prove special cases of these conjectures.

A family of diameter perfect constantweight codes from Steiner systems J. Comb. Theory A (IF 1.1) Pub Date : 20230731
Minjia Shi, Yuhong Xia, Denis S. KrotovIf S is a transitive metric space, then C⋅A≤S for any distanced code C and a set A, “anticode”, of diameter less than d. For every Steiner S(t,k,n) system S, we show the existence of a qary constantweight code C of length n, weight k (or n−k), and distance d=2k−t+1 (respectively, d=n−t+1) and an anticode A of diameter d−1 such that the pair (C,A) attains the code–anticode bound and the supports

Modifications of hyperplane arrangements J. Comb. Theory A (IF 1.1) Pub Date : 20230731
Houshan Fu, Suijie WangThis paper is concerned with five kinds of modification of hyperplane arrangements, including elementary lift, parallel translation, coning, oneelement extension and restriction to a hyperplane. We show that the combinatorial classification of all hyperplane arrangements of each kind of modification will be characterized by the intersection lattice of the discriminantal or adjoint arrangement. Based

Linear configurations containing 4term arithmetic progressions are uncommon J. Comb. Theory A (IF 1.1) Pub Date : 20230726
Leo VersteegenA linear configuration is said to be common in an Abelian group G if every 2coloring of G yields at least the number of monochromatic instances of a randomly chosen coloring. Saad and Wolf asked whether, analogously to a result by Jagger, Šťovíček and Thomason in graph theory, every configuration containing a 4term arithmetic progression is uncommon. We prove this in Fpn for p≥5 and large n and in

Hermitian matrices of roots of unity and their characteristic polynomials J. Comb. Theory A (IF 1.1) Pub Date : 20230720
We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by powers of (1−ζ), where ζ is a root of unity. We also prove a generalisation of a classical result of Harary and Schwenk about a relation for traces of powers of

Sum formulas for Schur multiple zeta values J. Comb. Theory A (IF 1.1) Pub Date : 20230718
In this paper, we study sum formulas for Schur multiple zeta values and give a generalization of the sum formulas for multiple zeta(star) values. We show that for ribbons of certain types, the sum of Schur multiple zeta values over all admissible Young tableaux of this shape evaluates to a rational multiple of the Riemann zeta value. For arbitrary ribbons with n corners, we show that such a sum can

A product version of the HiltonMilner theorem J. Comb. Theory A (IF 1.1) Pub Date : 20230717
Two families F,G of ksubsets of {1,2,…,n} are called nontrivial crossintersecting if F∩G≠∅ for all F∈F,G∈G and ∩{F:F∈F}=∅=∩{G:G∈G}. In the present paper, we determine the maximum product of the sizes of two nontrivial crossintersecting families of ksubsets of {1,2,…,n} for n≥4k, k≥8, which is a product version of the classical HiltonMilner Theorem.

Linked partition ideals and a family of quadruple summations J. Comb. Theory A (IF 1.1) Pub Date : 20230717
Recently, 4regular partitions into distinct parts were connected with a family of overpartitions. In this paper, we provide a uniform extension of two relations due to Andrews for the two types of partitions. Such an extension is made possible with recourse to a new trivariate Rogers–Ramanujan type identity, which concerns a family of quadruple summations appearing as generating functions for the

The first infinite family of orthogonal Steiner systems S(3,5,v) J. Comb. Theory A (IF 1.1) Pub Date : 20230704
Qianqian Yan, Junling ZhouThe research on orthogonal Steiner systems S(t,k,v) was initiated in 1968. For (t,k)∈{(2,3),(3,4)}, this corresponds to orthogonal Steiner triple systems (STSs) and Steiner quadruple systems (SQSs), respectively. The existence problem of a pair of orthogonal STSs or SQSs was settled completely thirty years ago. However, for Steiner systems with t≥3 and k≥5, only two small examples of orthogonal pairs

Ramsey nongoodness involving books J. Comb. Theory A (IF 1.1) Pub Date : 20230619
Chunchao Fan, Qizhong LinIn 1983, Burr and Erdős initiated the study of Ramsey goodness problems. Nikiforov and Rousseau (2009) resolved almost all goodness questions raised by Burr and Erdős, in which the bounds on the parameters are of tower type since their proofs rely on the regularity lemma. Let Bk,n be the book graph on n vertices which consists of n−k copies of Kk+1 all sharing a common Kk, and let H=Kp(a1,…,ap) be

Successive vertex orderings of fully regular graphs J. Comb. Theory A (IF 1.1) Pub Date : 20230612
Lixing Fang, Hao Huang, János Pach, Gábor Tardos, Junchi ZuoA graph G=(V,E) is called fully regular if for every independent set I⊂V, the number of vertices in V∖I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular

Cycles of evenodd drop permutations and continued fractions of Genocchi numbers J. Comb. Theory A (IF 1.1) Pub Date : 20230607
Qiongqiong Pan, Jiang ZengRecently Lazar and Wachs proved two new permutation models, called Dpermutations and Epermutations, for Genocchi and median Genocchi numbers. In a followup, Eu et al. studied the evenodd descent permutations, which are in bijection with Epermutations. We generalize Eu et al.'s descent polynomials with eight statistics and obtain an explicit Jfraction formula for their ordinary generaing function

Stirling permutation codes J. Comb. Theory A (IF 1.1) Pub Date : 20230601
ShiMei Ma, Hao Qi, Jean Yeh, YeongNan YehThe development of the theory of the secondorder Eulerian polynomials began with the works of Buckholtz and Carlitz in their studies of an asymptotic expansion. GesselStanley introduced Stirling permutations and provided combinatorial interpretations for the secondorder Eulerian polynomials in terms of Stirling permutations. The Stirling permutations have been extensively studied by many researchers

Further investigations on permutation based constructions of bent functions J. Comb. Theory A (IF 1.1) Pub Date : 20230601
Kangquan Li, Chunlei Li, Tor Helleseth, Longjiang QuConstructing bent functions by composing a Boolean function with a permutation was introduced by Hou and Langevin in 1997. The approach appears simple but heavily depends on the construction of desirable permutations. In this paper, we further study this approach by investigating the exponential sums of certain monomials and permutations. We propose several classes of bent functions from quadratic

Integer colorings with forbidden rainbow sums J. Comb. Theory A (IF 1.1) Pub Date : 20230523
Yangyang Cheng, Yifan Jing, Lina Li, Guanghui Wang, Wenling ZhouFor a set of positive integers A⊆[n], an rcoloring of A is rainbow sumfree if it contains no rainbow Schur triple. In this paper we initiate the study of the rainbow ErdősRothschild problem in the context of sumfree sets, which asks for the subsets of [n] with the maximum number of rainbow sumfree rcolorings. We show that for r=3, the interval [n] is optimal, while for r≥8, the set [⌊n/2⌋,n]


A Torelli theorem for graph isomorphisms J. Comb. Theory A (IF 1.1) Pub Date : 20230515
Sarah GriffithIt is known that isomorphisms of graph Jacobians induce cyclic bijections on the associated graphs. We characterize when such cyclic bijections can be strengthened to graph isomorphisms, in terms of an easily computed divisor. The result refines tools used in algebraic geometry to examine the fibers of the compactified Torelli map.

A Kruskal–Katonatype theorem for graphs: qKneser graphs J. Comb. Theory A (IF 1.1) Pub Date : 20230512
Jun Wang, Ao Xu, Huajun ZhangThe “KruskalKatonatype problem for a graph G” concerned here is to describe subsets of vertices of G that have minimum number of neighborhoods with respect to their sizes. In this paper, we establish a KruskalKatonatype theorem for the qKneser graphs, whose vertex set consists of all kdimensional subspaces of an ndimensional linear space over a qelement field, two subspaces are adjacent if

Regular Cayley maps of elementary abelian pgroups: Classification and enumeration J. Comb. Theory A (IF 1.1) Pub Date : 20230508
Shaofei Du, Hao Yu, Wenjuan LuoRecently, regular Cayley maps of cyclic groups and dihedral groups have been classified in [7] and [20], respectively. A nature question is to classify regular Cayley maps of elementary abelian pgroups Zpn. In this paper, a complete classification of regular Cayley maps of Zpn is given and moreover, the number of these maps and their genera are enumerated.

Embedding bipartite distance graphs under Hamming metric in finite fields J. Comb. Theory A (IF 1.1) Pub Date : 20230428
Zixiang Xu, Wenjun Yu, Gennian GeThe famous ErdősFalconer distance problems aim to quantify the extent to which large sets must determine many distinct distances. The problems in both the Euclidean setting and the discrete setting have received much attention. An interesting generalization of ErdősFalconer problems is to find locating point configurations with prescribed metric structure within large subsets. In this paper, we consider

Free fermions and Schur expansions of multiSchur functions J. Comb. Theory A (IF 1.1) Pub Date : 20230427
Shinsuke IwaoMultiSchur functions are symmetric functions that generalize the supersymmetric Schur functions, the flagged Schur functions, and the refined dual Grothendieck functions, which have been intensively studied by Lascoux. In this paper, we give a new freefermionic presentation of them. The multiSchur functions are indexed by a partition and two “tuples of tuples” of indeterminates. We construct a family

Nonexistence results of generalized bent functions from Z2n to Zm J. Comb. Theory A (IF 1.1) Pub Date : 20230425
Ka Hin Leung, Shuxing Li, Songtao MaoNew nonexistence results of generalized bent functions from Z2n to Zm are presented. In particular, we prove that there exists no generalized bent function from Z24 to Zm for every odd m.

Balancing permuted copies of multigraphs and integer matrices J. Comb. Theory A (IF 1.1) Pub Date : 20230412
Coen del Valle, Peter J. DukesGiven a square matrix A over the integers, we consider the Zmodule MA generated by the set of all matrices that are permutationsimilar to A. Motivated by analogous problems on signed graph decompositions and block designs, we are interested in the completely symmetric matrices aI+bJ belonging to MA. We give a relatively fast method to compute a generator for such matrices, avoiding the need for a

Activity from matroids to rooted trees and beyond J. Comb. Theory A (IF 1.1) Pub Date : 20230405
Rigoberto Flórez, David ForgeThe interior and exterior activities of bases of a matroid are wellknown notions that for instance permit one to define the Tutte polynomial. Recently, we have discovered correspondences between the regions of gainic hyperplane arrangements and colored labeled rooted trees. Here we define a general activity theory that applies in particular to nobroken circuit (NBC) sets and labeled colored trees


Indecomposable involutive solutions of the YangBaxter equation of multipermutation level 2 with nonabelian permutation group J. Comb. Theory A (IF 1.1) Pub Date : 20230323
Přemysl Jedlička, Agata PilitowskaWe give a complete characterization of all indecomposable involutive solutions of the YangBaxter equation of multipermutation level 2. In the first step we present a construction of some family of such solutions and in the second step we prove that every indecomposable involutive solution of the YangBaxter equation with multipermutation level 2 is a homomorphic image of a solution previously constructed

Orientablyregular pmaps and regular pmaps J. Comb. Theory A (IF 1.1) Pub Date : 20230322
Shaofei Du, Yao Tian, Xiaogang LiA map is called a pmap if it has a prime ppower vertices. An orientablyregular (resp. A regular) pmap is called solvable if the group G+ of all orientationpreserving automorphisms (resp. the group G of automorphisms) is solvable; and called normal if G+ (resp. G) contains the normal Sylow psubgroup. In this paper, it will be proved that both orientablyregular pmaps and regular pmaps are solvable

Symmetric generating functions and Euler–Stirling statistics on permutations J. Comb. Theory A (IF 1.1) Pub Date : 20230310
Emma Yu JinWe present (bi)symmetric generating functions for the joint distributions of Euler–Stirling statistics on permutations, including the number of descents (des), inverse descents (ides), the number of lefttoright maxima (lmax), the number of righttoleft maxima (rmax) and the number of lefttoright minima (lmin). We also show how they recover the classical symmetric generating function for permutations

A classification of flagtransitive 2(k2,k,λ) designs with λk J. Comb. Theory A (IF 1.1) Pub Date : 20230309
Alessandro MontinaroThe pairs (D,G), where D is a nontrivial 2(k2,k,λ) design with λk and G is a flagtransitive automorphism group of D are classified except for k a power of a prime and G⩽AΓL1(k2).

On the direct and inverse zerosum problems over Cn⋊sC2 J. Comb. Theory A (IF 1.1) Pub Date : 20230309
D.V. Avelar, F.E. Brochero Martínez, S. RibasLet Cn be the cyclic group of order n. In this paper, we provide the exact values of some zerosum constants over G=Cn⋊sC2 where s≢±1(modn), namely ηconstant, Gao constant, and ErdősGinzburgZiv constant (the latter for all but a “small” family of cases). As a consequence, we prove the Gao's and ZhuangGao's Conjectures for groups of this form. We also solve the associated inverse problems by characterizing

On Elser's conjecture and the topology of Unucleus complex J. Comb. Theory A (IF 1.1) Pub Date : 20230301
Apratim Chakraborty, Anupam Mondal, Sajal Mukherjee, Kuldeep SahaDorpalenBarry et al. proved Elser's conjecture about signs of Elser's numbers by interpreting them as certain sums of reduced Euler characteristic of an abstract simplicial complex known as Unucleus complex. We prove a conjecture posed by them regarding the homology of Unucleus complex.

Combinatorics of integer partitions with prescribed perimeter J. Comb. Theory A (IF 1.1) Pub Date : 20230302
Zhicong Lin, Huan Xiong, Sherry H.F. YanWe prove that the number of even parts and the number of times that parts are repeated have the same distribution over integer partitions with a fixed perimeter. This refines Straub's analog of Euler's OddDistinct partition theorem. We generalize the two concerned statistics to those of the partdifference less than d and the parts not congruent to 1 modulo d+1 and prove a distribution inequality

Graph schemes, graph series, and modularity J. Comb. Theory A (IF 1.1) Pub Date : 20230301
Kathrin Bringmann, Chris JenningsShaffer, Antun MilasTo a simple graph we associate a socalled graph series, which can be viewed as the Hilbert–Poincaré series of a certain infinite jet scheme. We study new qrepresentations and examine modular properties of several examples including Dynkin diagrams of finite and affine type. Notably, we obtain new formulas for graph series of type A7 and A8 in terms of “sum of tails” series, and of type D4 and D5

Stirling's approximation and a hidden link between two of Ramanujan's approximations J. Comb. Theory A (IF 1.1) Pub Date : 20230301
Cormac O'SullivanA conjectured relation between Ramanujan's asymptotic approximations to the exponential function and the exponential integral is established. The proof involves Stirling numbers, secondorder Eulerian numbers, modifications of both of these, and Stirling's approximation to the gamma function. Our work provides new information about the coefficients in Stirling's approximation and their connection to