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Boson operator ordering identities from generalized Stirling and Eulerian numbers Adv. Appl. Math. (IF 1.1) Pub Date : 20240214
Robert S. MaierOrdering identities in the Weyl–Heisenberg algebra generated by singlemode boson operators are investigated. A boson string composed of creation and annihilation operators can be expanded as a linear combination of other such strings, the simplest example being a normal ordering. The case when each string contains only one annihilation operator is already combinatorially nontrivial. Two kinds of expansion

Invariant differential derivations for reflection groups in positive characteristic Adv. Appl. Math. (IF 1.1) Pub Date : 20240212
D. Hanson, A.V. SheplerMuch of the captivating numerology surrounding finite reflection groups stems from Solomon's celebrated 1963 theorem describing invariant differential forms. Invariant differential derivations also exhibit fascinating numerology over the complex numbers linked to rational Catalan combinatorics. We explore the analogous theory over arbitrary fields, in particular, when the characteristic of the underlying

Two involutions on binary trees and generalizations Adv. Appl. Math. (IF 1.1) Pub Date : 20240209
Yang Li, Zhicong Lin, Tongyuan ZhaoThis paper investigates two involutions on binary trees. One is the mirror symmetry of binary trees which combined with the classical bijection between binary trees and plane trees answers an open problem posed by Bai and Chen. This involution can be generalized to weakly increasing trees, which admits to merge two recent equidistributions found by Bai–Chen and Chen–Fu, respectively. The other one


On the complexity of analyticity in semidefinite optimization Adv. Appl. Math. (IF 1.1) Pub Date : 20240209
Saugata Basu, Ali MohammadNezhadIt is wellknown that the central path of semidefinite optimization, unlike linear optimization, has no analytic extension to in the absence of the strict complementarity condition. In this paper, we consider a reparametrization , with being a positive integer, that recovers the analyticity of the central path at . We investigate the complexity of computing using algorithmic real algebraic geometry

NewtonOkounkov bodies of chemical reaction systems Adv. Appl. Math. (IF 1.1) Pub Date : 20240202
Nida Kazi Obatake, Elise WalkerDespite their noted potential in polynomialsystem solving, there are few concrete examples of NewtonOkounkov bodies arising from applications. Accordingly, in this paper, we introduce a new application of NewtonOkounkov body theory to the study of chemical reaction networks and compute several examples. An important invariant of a chemical reaction network is its maximum number of positive steady

A flow to the OrliczMinkowskitype problem of pcapacity Adv. Appl. Math. (IF 1.1) Pub Date : 20240202
Li Sheng, Jin YangThis article concerns the OrliczMinkowski problem for capacity for . We use the flow method to obtain a new existence result of solutions to this problem by an approximation argument for general measures.

Blockcounting sequences are not purely morphic Adv. Appl. Math. (IF 1.1) Pub Date : 20240201
Antoine Abram, Yining Hu, Shuo LiLet be a positive integer larger than 1, be a finite word over and represent the number of occurrences of the word in the expansion of the nonnegative integer (mod ). In this article, we present an efficient algorithm for generating all sequences ; then, assuming that is a prime number, we prove that all these sequences are uniformly but not purely morphic, except for words satisfying and ; finally

Generating functions and counting formulas for spanning trees and forests in hypergraphs Adv. Appl. Math. (IF 1.1) Pub Date : 20240116
Jiuqiang Liu, Shenggui Zhang, Guihai YuIn this paper, we provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs in two different ways: (1) We represent spanning trees and spanning forests in hypergraphs through BerezinGrassmann integrals on Zeon algebra and hyperHafnians (orders and signs are not considered); (2) We establish a HyperPfaffianCactus Spanning Forest Theorem through BerezinGrassmann

Connectivity of old and new models of friendsandstrangers graphs Adv. Appl. Math. (IF 1.1) Pub Date : 20240116
Aleksa MilojevićIn this paper, we investigate the connectivity of friendsandstrangers graphs, which were introduced by Defant and Kravitz in 2020. We begin by considering friendsandstrangers graphs arising from two random graphs and consider the threshold probability at which such graphs attain maximal connectivity. We slightly improve the lower bounds on the threshold probabilities, thus disproving two conjectures

Rowmotion Markov chains Adv. Appl. Math. (IF 1.1) Pub Date : 20240112
Colin Defant, Rupert Li, Evita NestoridiRowmotion is a certain wellstudied bijective operator on the distributive lattice J(P) of order ideals of a finite poset P. We introduce the rowmotion Markov chain MJ(P) by assigning a probability px to each x∈P and using these probabilities to insert randomness into the original definition of rowmotion. More generally, we introduce a very broad family of toggle Markov chains inspired by Striker's

Equidistribution of setvalued statistics on standard Young tableaux and transversals Adv. Appl. Math. (IF 1.1) Pub Date : 20240109
Robin D.P. Zhou, Sherry H.F. YanAs a natural generalization of permutations, transversals of Young diagrams play an important role in the study of pattern avoiding permutations. Let Tλ(τ) and STλ(τ) denote the set of τavoiding transversals and τavoiding symmetric transversals of a Young diagram λ, respectively. In this paper, we are mainly concerned with the distribution of the peak set and the valley set on standard Young tableaux

Pseudocones Adv. Appl. Math. (IF 1.1) Pub Date : 20240104
Rolf SchneiderPseudocones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counterpart to convex bodies containing the origin in the interior. The purpose of the following is to study this analogy in greater detail. We supplement the investigation of copolarity, considering, for example, conjugate faces

Moments of permutation statistics and central limit theorems Adv. Appl. Math. (IF 1.1) Pub Date : 20240105
Stoyan Dimitrov, Niraj KhareWe show that if a permutation statistic can be written as a linear combination of bivincular patterns, then its moments can be expressed as a linear combination of factorials with constant coefficients. This generalizes a result of Zeilberger. We use an approach of Chern, Diaconis, Kane and Rhoades, previously applied on set partitions and matchings. In addition, we give a new proof of the central


Identities and periodic oscillations of divideandconquer recurrences splitting at half Adv. Appl. Math. (IF 1.1) Pub Date : 20231229
HsienKuei Hwang, Svante Janson, TsungHsi TsaiWe study divideandconquer recurrences of the formf(n)=αf(⌊n2⌋)+βf(⌈n2⌉)+g(n)(n⩾2), with g(n) and f(1) given, where α,β⩾0 with α+β>0; such recurrences appear often in the analysis of computer algorithms, numeration systems, combinatorial sequences, and related areas. We show under an optimum (iff) condition on g(n) that the solution f always satisfies a simple identityf(n)=nlog2(α+β)P(log2n)−Q(n)

An inversion statistic on the generalized symmetric groups Adv. Appl. Math. (IF 1.1) Pub Date : 20231222
Hasan Arslan, Alnour Altoum, Mariam ZaarourIn this paper, we construct a mixedbase number system over the generalized symmetric group G(m,1,n), which is a complex reflection group with a root system of type Bn(m). We also establish onetoone correspondence between all positive integers in the set {1,⋯,mnn!} and the elements of G(m,1,n) by constructing the subexceedant function in relation to this group. In addition, we provide a new enumeration

Enumeration of antiinvariant subspaces and Touchard's formula for the entries of the qHermite Catalan matrix Adv. Appl. Math. (IF 1.1) Pub Date : 20231220
Amritanshu Prasad, Samrith RamWe express the number of antiinvariant subspaces for a linear operator on a finite vector space in terms of the number of its invariant subspaces. When the operator is diagonalizable with distinct eigenvalues, our formula gives a finitefield interpretation for the entries of the qHermite Catalan matrix. We also obtain an interesting new proof of Touchard's formula for these entries.

Stable fixed points of combinatorial thresholdlinear networks Adv. Appl. Math. (IF 1.1) Pub Date : 20231213
Carina Curto, Jesse Geneson, Katherine MorrisonCombinatorial thresholdlinear networks (CTLNs) are a special class of recurrent neural networks whose dynamics are tightly controlled by an underlying directed graph. Recurrent networks have long been used as models for associative memory and pattern completion, with stable fixed points playing the role of stored memory patterns in the network. In prior work, we showed that targetfree cliques of

The image of the pop operator on various lattices Adv. Appl. Math. (IF 1.1) Pub Date : 20231207
Yunseo Choi, Nathan SunExtending the classical popstack sorting map on the lattice given by the right weak order on Sn, Defant defined, for any lattice M, a map PopM:M→M that sends an element x∈M to the meet of x and the elements covered by x. In parallel with the line of studies on the image of the classical popstack sorting map, we study PopM(M) when M is the weak order of type Bn, the Tamari lattice of type Bn, the

Connectivity gaps among matroids with the same enumerative invariants Adv. Appl. Math. (IF 1.1) Pub Date : 20231208
Joseph E. Bonin, Kevin LongMany important enumerative invariants of a matroid can be obtained from its Tutte polynomial, and many more are determined by two stronger invariants, the Ginvariant and the configuration of the matroid. We show that the same is not true of the most basic connectivity invariants. Specifically, we show that for any positive integer n, there are pairs of matroids that have the same configuration (and

Can a single migrant per generation rescue a dying population? Adv. Appl. Math. (IF 1.1) Pub Date : 20231207
Iddo BenAri, Rinaldo B. SchinaziWe introduce a population model to test the hypothesis that even a single migrant per generation may rescue a dying population. Let (ck:k∈N) be a sequence of real numbers in (0,1). Let Xn be a size of the population at time n≥0. Then, Xn+1=Xn−Yn+1+1, where the conditional distribution of Yn+1 given Xn=k is a binomial random variable with parameters (k,c(k)). We assume that limk→∞kc(k)=ρ exists. If

Properties arising from LaguerrePólya class for the BorosMoll numbers Adv. Appl. Math. (IF 1.1) Pub Date : 20231129
Jungle Z.X. Jiang, Larry X.W. WangThe BorosMoll numbers di(m) arise from a quartic integral studied by Boros and Moll. For fixed m, the sequence {di(m)}0≤i≤m has been proven to satisfy the Turán inequality, the higher order Turán inequality and 3logconcavity which are originated from the LaguerrePólya class. In this paper, we give sharper bounds for both di(m+1)/di(m) and di(m)2/(di−1(m)di+1(m)). Applying these bounds, we prove

qfractional integral operators with two parameters Adv. Appl. Math. (IF 1.1) Pub Date : 20231127
Mourad E.H. Ismail, Keru ZhouWe use the Poisson kernel of the continuous qHermite polynomials to introduce families of integral operators. One of them is semigroups of linear operators. We describe the eigenvalues and eigenfunctions of one family of operators. The action of the semigroups of operators on the Askey–Wilson polynomials is shown to only change the parameters but preserves the degrees, hence we produce transmutation

Continuity of limit surfaces of locally uniform random permutations Adv. Appl. Math. (IF 1.1) Pub Date : 20231128
Jonas SjöstrandA locally uniform random permutation is generated by sampling n points independently from some absolutely continuous distribution ρ on the plane and interpreting them as a permutation by the rule that i maps to j if the ith point from the left is the jth point from below. As n tends to infinity, decreasing subsequences in the permutation will appear as curves in the plane, and by interpreting these


The entropy of the radical ideal of a tropical curve Adv. Appl. Math. (IF 1.1) Pub Date : 20231114
Dima GrigorievThe entropy of a semiring ideal of tropical polynomials is introduced. The radical of a semiring ideal consists of all tropical polynomials vanishing on the tropical prevariety determined by the ideal. We prove that the entropy of the radical of a tropical bivariate polynomial with zero coefficients vanishes. Also, we prove that the entropy of a zerodimensional tropical prevariety vanishes. An example

HarderNarasimhan filtrations and zigzag persistence Adv. Appl. Math. (IF 1.1) Pub Date : 20231107
Marc Fersztand, Vidit Nanda, Ulrike TillmannWe introduce a sheaftheoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type A˜ quivers, there is a precise relationship between the associated HarderNarasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.

Invariants for level1 phylogenetic networks under the CavendarFarrisNeyman model Adv. Appl. Math. (IF 1.1) Pub Date : 20231027
Joseph Cummings, Benjamin Hollering, Christopher ManonPhylogenetic networks model evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. The same Markov models used for sequence evolution on trees can also be extended to networks and similar problems, such as determining if the network parameter is identifiable or finding the invariants of the model, can be studied. This paper focuses on finding the invariants

Alternatives for the qmatroid axioms of independent spaces, bases, and spanning spaces Adv. Appl. Math. (IF 1.1) Pub Date : 20231025
Michela Ceria, Relinde JurriusIt is well known that in qmatroids, axioms for independent spaces, bases, and spanning spaces differ from the classical case of matroids, since the straightforward qanalogue of the classical axioms does not give a qmatroid. For this reason, a fourth axiom has been proposed. In this paper we show how we can describe these spaces with only three axioms, providing two alternative ways to do that. As

Chordal matroids arising from generalized parallel connections Adv. Appl. Math. (IF 1.1) Pub Date : 20231023
James Dylan Douthitt, James OxleyA graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated cliquesums. Generalizing this, we consider the class of simple GF(q)representable matroids that can be built from projective geometries over GF(q) by repeated generalized parallel connections across projective geometries

A note on Cauchy's formula Adv. Appl. Math. (IF 1.1) Pub Date : 20231017
Naihuan Jing, Zhijun LiWe use the correlation functions of vertex operators to give a proof of Cauchy's formula∏i=1K∏j=1N(1−xiyj)=∑μ⊆[K×N](−1)μsμ{x}sμ′{y}. As an application of the interpretation, we obtain an expansion of ∏i=1∞(1−qi)i−1 in terms of half plane partitions.

Extended higher Herglotz functions I. Functional equations Adv. Appl. Math. (IF 1.1) Pub Date : 20231012
Atul Dixit, Rajat Gupta, Rahul KumarIn 1975, Don Zagier obtained a new version of the Kronecker limit formula for a real quadratic field which involved an interesting function F(x) which is now known as the Herglotz function. As demonstrated by Zagier, and very recently by Radchenko and Zagier, F(x) satisfies beautiful properties which are of interest in both algebraic number theory as well as in analytic number theory. In this paper

Realisations of Racah algebras using Jacobi operators and convolution identities Adv. Appl. Math. (IF 1.1) Pub Date : 20231011
Q. Labriet, L. Poulain d'AndecyUsing the representation theory of sl2 and an appropriate model for tensor product of lowest weight Verma modules, we give a realisation first of the Hahn algebra, and then of the Racah algebra, using Jacobi differential operators. While doing so we recover some known convolution formulas for Jacobi polynomials involving Hahn and Racah polynomials. Similarly, we produce realisations of the higher rank

The floor quotient partial order Adv. Appl. Math. (IF 1.1) Pub Date : 20231012
Jeffrey C. Lagarias, David Harry RichmanA positive integer d is a floor quotient of n if there is a positive integer k such that d=⌊n/k⌋. The floor quotient relation defines a partial order on the positive integers. This paper studies the internal structure of this partial order and its Möbius function.

Clustering and ArnouxRauzy words Adv. Appl. Math. (IF 1.1) Pub Date : 20231004
Sébastien Ferenczi, Luca Q. ZamboniWe characterize the clustering of a word under the BurrowsWheeler transform in terms of the resolution of a bounded number of bispecial factors belonging to the language generated by all its powers. We use this criterion to compute, in every given ArnouxRauzy language on three letters, an explicit bound K such that each word of length at least K is not clustering; this bound is sharp for a set of

Partialtwuality polynomials of deltamatroids Adv. Appl. Math. (IF 1.1) Pub Date : 20231004
Qi Yan, Xian'an JinGross, Mansour and Tucker introduced the partialtwuality polynomial of a ribbon graph. Chumutov and VignesTourneret posed a problem: it would be interesting to know whether the partial duality polynomial and the related conjectures would make sense for general deltamatroids. In this paper we consider analogues of partialtwuality polynomials for deltamatroids. Various possible properties of partialtwuality

Action of Hecke algebra on the double flag variety of type AIII Adv. Appl. Math. (IF 1.1) Pub Date : 20230925
Lucas Fresse, Kyo NishiyamaConsider a connected reductive algebraic group G and a symmetric subgroup K. Let X=K/BK×G/P be a double flag variety of finite type, where BK is a Borel subgroup of K, and P a parabolic subgroup of G. A general argument shows that the orbit space CX/K inherits a natural action of the Hecke algebra H=H(K,BK) of double cosets via convolutions. However, it is a quite different problem to find out the

Rotational Crofton formulae with a fixed subspace Adv. Appl. Math. (IF 1.1) Pub Date : 20230921
Emil Dare, Markus KiderlenThe classical Crofton formula explains how intrinsic volumes of a convex body K in ndimensional Euclidean space can be obtained from integrating a measurement function at sections of K with invariantly moved affine flats. Motivated by stereological applications, we present variants of Crofton's formula, where the flats are constrained to contain a fixed linear subspace L0, but are otherwise invariantly

Bijections between the multifurcating unlabeled rooted trees and the positive integers Adv. Appl. Math. (IF 1.1) Pub Date : 20230921
Alessandra Rister Portinari Maranca, Noah A. RosenbergColijn and Plazzotta (2018) [1] described a bijective scheme for associating the unlabeled bifurcating rooted trees with the positive integers. In mathematical and biological applications of unlabeled rooted trees, however, nodes of rooted trees are sometimes multifurcating rather than bifurcating. Building on the bijection between the unlabeled bifurcating rooted trees and the positive integers, we

Somos4 equation and related equations Adv. Appl. Math. (IF 1.1) Pub Date : 20230921
Andrei K. SvininThe main object of study in this paper is the wellknown Somos4 recurrence. We prove a theorem that any sequence generated by this equation also satisfies GaleRobinson one. The corresponding identity is written in terms of its companion elliptic sequence. An example of such relationship is provided by the secondorder linear sequence which, as we prove using Wajda's identity, satisfies the Somos4

Apérytype series and colored multiple zeta values Adv. Appl. Math. (IF 1.1) Pub Date : 20230921
Ce Xu, Jianqiang ZhaoIn this paper, we study new classes of Apérytype series involving the central binomial coefficients and the multiple tharmonic sums by combining the methods of iterated integrals and Fourier–Legendre series expansions, where the multiple tharmonic sums are a variation of multiple harmonic sums in which all the summation indices are restricted to odd numbers only. Our approach also enables us to

Rational local unitary invariants of symmetrically mixed states of two qubits Adv. Appl. Math. (IF 1.1) Pub Date : 20230918
Luca Candelori, Vladimir Y. Chernyak, John R. Klein, Nick RekuskiWe compute the field of rational local unitary invariants for locally maximally mixed states and symmetrically mixed states of two qubits. In both cases, we prove that the field of rational invariants is purely transcendental. We also construct explicit geometric quotients and prove that they are always rational. All the results are obtained by working over the field of real numbers, employing methods

qRational and qreal binomial coefficients Adv. Appl. Math. (IF 1.1) Pub Date : 20230918
John Machacek, Nicholas OvenhouseWe consider qbinomial coefficients built from the qrational and qreal numbers defined by MorierGenoud and Ovsienko in terms of continued fractions. We establish versions of both the qPascal identity and the qbinomial theorem in this setting. These results are then used to find more identities satisfied by the qanalogues of MorierGenoud and Ovsienko, including a Chu–Vandermonde identity and

Supersolvable saturated matroids and chordal graphs Adv. Appl. Math. (IF 1.1) Pub Date : 20230918
Dillon Mayhew, Andrew ProbertA matroid is supersolvable if it has a maximal chain of flats, each of which is modular. A matroid is saturated if every round flat is modular. In this article we present supersolvable saturated matroids as analogues to chordal graphs, and we show that several results for chordal graphs hold in this matroidal context. In particular, we consider matroid analogues of the reduced clique graph and clique

Multiple partition structures and harmonic functions on branching graphs Adv. Appl. Math. (IF 1.1) Pub Date : 20230920
Eugene StrahovWe introduce and study multiple partition structures which are sequences of probability measures on families of Young diagrams subjected to a consistency condition. The multiple partition structures are generalizations of Kingman's partition structures, and are motivated by a problem of population genetics. They are related to harmonic functions and coherent systems of probability measures on a certain

Character analogues of Cohentype identities and related Voronoï summation formulas Adv. Appl. Math. (IF 1.1) Pub Date : 20230918
Debika Banerjee, Khyati KhuranaIn [4], B. C. Berndt and A. Zaharescu introduced the twisted divisor sums associated with the Dirichlet character while studying the Ramanujan's type identity involving finite trigonometric sums and doubly infinite series of Bessel functions. Later, in a followup paper [20], S. Kim extended the definition of the twisted divisor sums to twisted sums of divisor functions. In this paper, we derive identities

Corrigendum to “Twodimensional Fibonacci words: Tandem repeats and factor complexity” [Adv. Appl. Math. 149 (2023) 102553] Adv. Appl. Math. (IF 1.1) Pub Date : 20230906
M. Sivasankar, R. RamaAbstract not available

Counting derangements with signed righttoleft minima and excedances Adv. Appl. Math. (IF 1.1) Pub Date : 20230901
Yanni Pei, Jiang ZengRecently Alexandersson and Getachew proved some multivariate generalizations of a formula for enumerating signed excedances in derangements. In this paper we first relate their work to a recent continued fraction for permutations and confirm some of their observations. Our second main result is two refinements of their multivariate identities, which clearly explain the meaning of each term in their

Carries and a map on the space of rational functions Adv. Appl. Math. (IF 1.1) Pub Date : 20230830
Jason FulmanA paper by Boros, Little, Moll, Mosteig, and Stanley relates properties of a map defined on the space of rational functions to Eulerian polynomials. We link their work to the carries Markov chain, giving a new proof and slight generalization of one of their results.

Inequalities for the overpartition function arising from determinants Adv. Appl. Math. (IF 1.1) Pub Date : 20230829
Gargi MukherjeeLet p‾(n) denote the overpartition function. This paper presents the 2logconcavity property of p‾(n) by considering a more general inequality of the following formp‾(n)p‾(n+1)p‾(n+2)p‾(n−1)p‾(n)p‾(n+1)p‾(n−2)p‾(n−1)p‾(n)>0, which holds for all n≥42.

The distributions under two speciestree models of the total number of ancestral configurations for matching gene trees and species trees Adv. Appl. Math. (IF 1.1) Pub Date : 20230816
Filippo Disanto, Michael Fuchs, ChunYen Huang, Ariel R. Paningbatan, Noah A. RosenbergGiven a genetree labeled topology G and a species tree S, the ancestral configurations at an internal node k of S represent the combinatorially different sets of gene lineages that can be present at k when all possible realizations of G in S are considered. Ancestral configurations have been introduced as a data structure for evaluating the conditional probability of a genetree labeled topology given

Hypercubes and Hamilton cycles of display sets of rooted phylogenetic networks Adv. Appl. Math. (IF 1.1) Pub Date : 20230808
Janosch Döcker, Simone Linz, Charles SempleIn the context of reconstructing phylogenetic networks from a collection of phylogenetic trees, several characterisations and subsequently algorithms have been established to reconstruct a phylogenetic network that collectively embeds all trees in the input in some minimum way. For many instances however, the resulting network also embeds additional phylogenetic trees that are not part of the input

Toric rings arising from vertex cover ideals Adv. Appl. Math. (IF 1.1) Pub Date : 20230807
Jürgen Herzog, Takayuki Hibi, Somayeh MoradiWe extend the sortability concept to monomial ideals which are not necessarily generated in one degree and as an application we obtain normal CohenMacaulay toric rings attached to vertex cover ideals of graphs. Moreover, we consider a construction on a graph called a clique multiwhiskering which always produces vertex cover ideals with componentwise linear powers.

Euclidean distance degree and limit points in a Morsification Adv. Appl. Math. (IF 1.1) Pub Date : 20230807
Laurenţiu Maxim, Mihai TibărMotivated by finding an effective way to compute the algebraic complexity of the nearest point problem for algebraic models, we introduce an efficient method for detecting the limit points of the stratified Morse trajectories in a small perturbation of any polynomial function on a complex affine variety. We compute the multiplicities of these limit points in terms of vanishing cycles. In the case of

Some results related to Hurwitz stability of combinatorial polynomials Adv. Appl. Math. (IF 1.1) Pub Date : 20230728
MingJian Ding, BaoXuan ZhuMany important problems are closely related to the zeros of certain polynomials derived from combinatorial objects. The aim of this paper is to observe some results and applications for the Hurwitz stability of polynomials in combinatorics and study other related problems. We first present a criterion for the Hurwitz stability of the Turán expressions of recursive polynomials. In particular, it implies

A unified framework to prove multiplicative inequalities for the partition function Adv. Appl. Math. (IF 1.1) Pub Date : 20230728
Koustav BanerjeeIn this paper, we consider a certain class of inequalities for the partition function of the following form:∏i=1Tp(n+si)≥∏i=1Tp(n+ri), which we call multiplicative inequalities. Given a multiplicative inequality with the condition that ∑i=1Tsim≠∑i=1Trim for at least one m≥1, we shall construct a unified framework so as to decide whether such a inequality holds or not. As a consequence, we will see

Rota's basis conjecture for matroids with density close to one Adv. Appl. Math. (IF 1.1) Pub Date : 20230726
Sean McGuinnessRota's basis conjecture (RBC) states that given a collection B of n bases in a matroid M of rank n, one can always find n disjoint rainbow bases with respect to B. We show that if M is a matroid having n+k elements, then one can construct n−k3 disjoint rainbow bases.

Generic local rings on a spectrum between Golod and Gorenstein Adv. Appl. Math. (IF 1.1) Pub Date : 20230719
Artinian quotients R of the local ring Q=k[[x,y,z]] are classified by multiplicative structures on A=Tor⁎Q(R,k); in particular, R is Gorenstein if and only if A is a Poincaré duality algebra while R is Golod if and only if all products in A⩾1 are trivial. There is empirical evidence that generic quotient rings with small socle ranks fall on a spectrum between Golod and Gorenstein in a very precise

kFactorizations of the full cycle and generalized Mahonian statistics on kforests Adv. Appl. Math. (IF 1.1) Pub Date : 20230717
We develop direct bijections between the set Fnk of minimal factorizations of the long cycle (01⋯kn) into (k+1)cycle factors and the set Rnk of rooted labelled forests on vertices {1,…,n} with edges coloured with {0,1,…,k−1} that map natural statistics on the former to generalized Mahonian statistics on the latter. In particular, we examine the generalized major index on forests Rnk and show that