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On the recursive and explicit form of the general J.C.P. Miller formula with applications Adv. Appl. Math. (IF 1.1) Pub Date : 2024-03-12 Dariusz Bugajewski, Dawid Bugajewski, Xiao-Xiong Gan, Piotr Maćkowiak
The famous J.C.P. Miller formula provides a recurrence algorithm for the composition , where is the formal binomial series and is a formal power series, however it requires that has to be a nonunit.
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Substitution-dynamics and invariant measures for infinite alphabet-path space Adv. Appl. Math. (IF 1.1) Pub Date : 2024-03-12 Sergey Bezuglyi, Palle E.T. Jorgensen, Shrey Sanadhya
We study substitutions on a countably infinite alphabet (without compactification) as Borel dynamical systems. We construct stationary and non-stationary generalized Bratteli-Vershik models for a class of such substitutions, known as . In this setting of Borel dynamics, using a stationary generalized Bratteli-Vershik model, we provide a new and canonical construction of shift-invariant measures (both
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Certain extensions of results of Siegel, Wilton and Hardy Adv. Appl. Math. (IF 1.1) Pub Date : 2024-03-12 Pedro Ribeiro, Semyon Yakubovich
Recently, Dixit et al. established a very elegant generalization of Hardy's theorem concerning the infinitude of zeros that the Riemann zeta function possesses at its critical line.
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Wilf equivalences for patterns in rooted labeled forests Adv. Appl. Math. (IF 1.1) Pub Date : 2024-03-04 Michael Ren
Building off recent work of Garg and Peng, we continue the investigation into classical and consecutive pattern avoidance in rooted forests, resolving some of their conjectures and questions and proving generalizations whenever possible. Through extensions of the forest Simion-Schmidt bijection introduced by Anders and Archer, we demonstrate a new family of forest-Wilf equivalences, completing the
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Boson operator ordering identities from generalized Stirling and Eulerian numbers Adv. Appl. Math. (IF 1.1) Pub Date : 2024-02-14 Robert S. Maier
Ordering identities in the Weyl–Heisenberg algebra generated by single-mode 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
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Invariant differential derivations for reflection groups in positive characteristic Adv. Appl. Math. (IF 1.1) Pub Date : 2024-02-12 D. Hanson, A.V. Shepler
Much 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
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Two involutions on binary trees and generalizations Adv. Appl. Math. (IF 1.1) Pub Date : 2024-02-09 Yang Li, Zhicong Lin, Tongyuan Zhao
This 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
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On the complexity of analyticity in semi-definite optimization Adv. Appl. Math. (IF 1.1) Pub Date : 2024-02-09 Saugata Basu, Ali Mohammad-Nezhad
It is well-known that the central path of semi-definite 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
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Newton-Okounkov bodies of chemical reaction systems Adv. Appl. Math. (IF 1.1) Pub Date : 2024-02-02 Nida Kazi Obatake, Elise Walker
Despite their noted potential in polynomial-system solving, there are few concrete examples of Newton-Okounkov bodies arising from applications. Accordingly, in this paper, we introduce a new application of Newton-Okounkov 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
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A flow to the Orlicz-Minkowski-type problem of p-capacity Adv. Appl. Math. (IF 1.1) Pub Date : 2024-02-02 Li Sheng, Jin Yang
This article concerns the Orlicz-Minkowski 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.
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Block-counting sequences are not purely morphic Adv. Appl. Math. (IF 1.1) Pub Date : 2024-02-01 Antoine Abram, Yining Hu, Shuo Li
Let 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 non-negative 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
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Generating functions and counting formulas for spanning trees and forests in hypergraphs Adv. Appl. Math. (IF 1.1) Pub Date : 2024-01-16 Jiuqiang Liu, Shenggui Zhang, Guihai Yu
In 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 Berezin-Grassmann integrals on Zeon algebra and hyper-Hafnians (orders and signs are not considered); (2) We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann
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Connectivity of old and new models of friends-and-strangers graphs Adv. Appl. Math. (IF 1.1) Pub Date : 2024-01-16 Aleksa Milojević
In this paper, we investigate the connectivity of friends-and-strangers graphs, which were introduced by Defant and Kravitz in 2020. We begin by considering friends-and-strangers 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
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Rowmotion Markov chains Adv. Appl. Math. (IF 1.1) Pub Date : 2024-01-12 Colin Defant, Rupert Li, Evita Nestoridi
Rowmotion is a certain well-studied 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
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Equidistribution of set-valued statistics on standard Young tableaux and transversals Adv. Appl. Math. (IF 1.1) Pub Date : 2024-01-09 Robin D.P. Zhou, Sherry H.F. Yan
As 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 τ-avoiding transversals and τ-avoiding 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
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Pseudo-cones Adv. Appl. Math. (IF 1.1) Pub Date : 2024-01-04 Rolf Schneider
Pseudo-cones 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
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Moments of permutation statistics and central limit theorems Adv. Appl. Math. (IF 1.1) Pub Date : 2024-01-05 Stoyan Dimitrov, Niraj Khare
We 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
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Identities and periodic oscillations of divide-and-conquer recurrences splitting at half Adv. Appl. Math. (IF 1.1) Pub Date : 2023-12-29 Hsien-Kuei Hwang, Svante Janson, Tsung-Hsi Tsai
We study divide-and-conquer 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)
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An inversion statistic on the generalized symmetric groups Adv. Appl. Math. (IF 1.1) Pub Date : 2023-12-22 Hasan Arslan, Alnour Altoum, Mariam Zaarour
In this paper, we construct a mixed-base 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 one-to-one 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
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Enumeration of anti-invariant subspaces and Touchard's formula for the entries of the q-Hermite Catalan matrix Adv. Appl. Math. (IF 1.1) Pub Date : 2023-12-20 Amritanshu Prasad, Samrith Ram
We express the number of anti-invariant 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 finite-field interpretation for the entries of the q-Hermite Catalan matrix. We also obtain an interesting new proof of Touchard's formula for these entries.
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Stable fixed points of combinatorial threshold-linear networks Adv. Appl. Math. (IF 1.1) Pub Date : 2023-12-13 Carina Curto, Jesse Geneson, Katherine Morrison
Combinatorial threshold-linear 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 target-free cliques of
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The image of the pop operator on various lattices Adv. Appl. Math. (IF 1.1) Pub Date : 2023-12-07 Yunseo Choi, Nathan Sun
Extending the classical pop-stack 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 pop-stack sorting map, we study PopM(M) when M is the weak order of type Bn, the Tamari lattice of type Bn, the
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Connectivity gaps among matroids with the same enumerative invariants Adv. Appl. Math. (IF 1.1) Pub Date : 2023-12-08 Joseph E. Bonin, Kevin Long
Many important enumerative invariants of a matroid can be obtained from its Tutte polynomial, and many more are determined by two stronger invariants, the G-invariant 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
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Can a single migrant per generation rescue a dying population? Adv. Appl. Math. (IF 1.1) Pub Date : 2023-12-07 Iddo Ben-Ari, Rinaldo B. Schinazi
We 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
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Properties arising from Laguerre-Pólya class for the Boros-Moll numbers Adv. Appl. Math. (IF 1.1) Pub Date : 2023-11-29 Jungle Z.X. Jiang, Larry X.W. Wang
The Boros-Moll 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 3-log-concavity which are originated from the Laguerre-Pólya 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
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q-fractional integral operators with two parameters Adv. Appl. Math. (IF 1.1) Pub Date : 2023-11-27 Mourad E.H. Ismail, Keru Zhou
We use the Poisson kernel of the continuous q-Hermite 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
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Continuity of limit surfaces of locally uniform random permutations Adv. Appl. Math. (IF 1.1) Pub Date : 2023-11-28 Jonas Sjöstrand
A 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
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The entropy of the radical ideal of a tropical curve Adv. Appl. Math. (IF 1.1) Pub Date : 2023-11-14 Dima Grigoriev
The 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 zero-dimensional tropical prevariety vanishes. An example
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Harder-Narasimhan filtrations and zigzag persistence Adv. Appl. Math. (IF 1.1) Pub Date : 2023-11-07 Marc Fersztand, Vidit Nanda, Ulrike Tillmann
We introduce a sheaf-theoretic 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 Harder-Narasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.
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Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman model Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-27 Joseph Cummings, Benjamin Hollering, Christopher Manon
Phylogenetic 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
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Alternatives for the q-matroid axioms of independent spaces, bases, and spanning spaces Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-25 Michela Ceria, Relinde Jurrius
It is well known that in q-matroids, axioms for independent spaces, bases, and spanning spaces differ from the classical case of matroids, since the straightforward q-analogue of the classical axioms does not give a q-matroid. 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
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Chordal matroids arising from generalized parallel connections Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-23 James Dylan Douthitt, James Oxley
A 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 clique-sums. 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
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A note on Cauchy's formula Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-17 Naihuan Jing, Zhijun Li
We 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)|μ|sμ{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.
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Extended higher Herglotz functions I. Functional equations Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-12 Atul Dixit, Rajat Gupta, Rahul Kumar
In 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
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Realisations of Racah algebras using Jacobi operators and convolution identities Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-11 Q. Labriet, L. Poulain d'Andecy
Using 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
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The floor quotient partial order Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-12 Jeffrey C. Lagarias, David Harry Richman
A 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.
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Clustering and Arnoux-Rauzy words Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-04 Sébastien Ferenczi, Luca Q. Zamboni
We characterize the clustering of a word under the Burrows-Wheeler 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 Arnoux-Rauzy 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
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Partial-twuality polynomials of delta-matroids Adv. Appl. Math. (IF 1.1) Pub Date : 2023-10-04 Qi Yan, Xian'an Jin
Gross, Mansour and Tucker introduced the partial-twuality polynomial of a ribbon graph. Chumutov and Vignes-Tourneret posed a problem: it would be interesting to know whether the partial duality polynomial and the related conjectures would make sense for general delta-matroids. In this paper we consider analogues of partial-twuality polynomials for delta-matroids. Various possible properties of partial-twuality
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Action of Hecke algebra on the double flag variety of type AIII Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-25 Lucas Fresse, Kyo Nishiyama
Consider 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
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Rotational Crofton formulae with a fixed subspace Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-21 Emil Dare, Markus Kiderlen
The classical Crofton formula explains how intrinsic volumes of a convex body K in n-dimensional 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
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Bijections between the multifurcating unlabeled rooted trees and the positive integers Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-21 Alessandra Rister Portinari Maranca, Noah A. Rosenberg
Colijn 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
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Somos-4 equation and related equations Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-21 Andrei K. Svinin
The main object of study in this paper is the well-known Somos-4 recurrence. We prove a theorem that any sequence generated by this equation also satisfies Gale-Robinson one. The corresponding identity is written in terms of its companion elliptic sequence. An example of such relationship is provided by the second-order linear sequence which, as we prove using Wajda's identity, satisfies the Somos-4
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Apéry-type series and colored multiple zeta values Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-21 Ce Xu, Jianqiang Zhao
In this paper, we study new classes of Apéry-type series involving the central binomial coefficients and the multiple t-harmonic sums by combining the methods of iterated integrals and Fourier–Legendre series expansions, where the multiple t-harmonic 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
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Rational local unitary invariants of symmetrically mixed states of two qubits Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-18 Luca Candelori, Vladimir Y. Chernyak, John R. Klein, Nick Rekuski
We 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
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q-Rational and q-real binomial coefficients Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-18 John Machacek, Nicholas Ovenhouse
We consider q-binomial coefficients built from the q-rational and q-real numbers defined by Morier-Genoud and Ovsienko in terms of continued fractions. We establish versions of both the q-Pascal identity and the q-binomial theorem in this setting. These results are then used to find more identities satisfied by the q-analogues of Morier-Genoud and Ovsienko, including a Chu–Vandermonde identity and
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Supersolvable saturated matroids and chordal graphs Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-18 Dillon Mayhew, Andrew Probert
A 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
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Multiple partition structures and harmonic functions on branching graphs Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-20 Eugene Strahov
We 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
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Character analogues of Cohen-type identities and related Voronoï summation formulas Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-18 Debika Banerjee, Khyati Khurana
In [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 follow-up paper [20], S. Kim extended the definition of the twisted divisor sums to twisted sums of divisor functions. In this paper, we derive identities
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Corrigendum to “Two-dimensional Fibonacci words: Tandem repeats and factor complexity” [Adv. Appl. Math. 149 (2023) 102553] Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-06 M. Sivasankar, R. Rama
Abstract not available
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Counting derangements with signed right-to-left minima and excedances Adv. Appl. Math. (IF 1.1) Pub Date : 2023-09-01 Yanni Pei, Jiang Zeng
Recently 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
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Carries and a map on the space of rational functions Adv. Appl. Math. (IF 1.1) Pub Date : 2023-08-30 Jason Fulman
A 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.
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Inequalities for the overpartition function arising from determinants Adv. Appl. Math. (IF 1.1) Pub Date : 2023-08-29 Gargi Mukherjee
Let p‾(n) denote the overpartition function. This paper presents the 2-log-concavity property of p‾(n) by considering a more general inequality of the following form|p‾(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.
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The distributions under two species-tree models of the total number of ancestral configurations for matching gene trees and species trees Adv. Appl. Math. (IF 1.1) Pub Date : 2023-08-16 Filippo Disanto, Michael Fuchs, Chun-Yen Huang, Ariel R. Paningbatan, Noah A. Rosenberg
Given a gene-tree 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 gene-tree labeled topology given
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Hypercubes and Hamilton cycles of display sets of rooted phylogenetic networks Adv. Appl. Math. (IF 1.1) Pub Date : 2023-08-08 Janosch Döcker, Simone Linz, Charles Semple
In 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
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Toric rings arising from vertex cover ideals Adv. Appl. Math. (IF 1.1) Pub Date : 2023-08-07 Jürgen Herzog, Takayuki Hibi, Somayeh Moradi
We extend the sortability concept to monomial ideals which are not necessarily generated in one degree and as an application we obtain normal Cohen-Macaulay toric rings attached to vertex cover ideals of graphs. Moreover, we consider a construction on a graph called a clique multi-whiskering which always produces vertex cover ideals with componentwise linear powers.
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Euclidean distance degree and limit points in a Morsification Adv. Appl. Math. (IF 1.1) Pub Date : 2023-08-07 Laurenţiu Maxim, Mihai Tibăr
Motivated 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
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Some results related to Hurwitz stability of combinatorial polynomials Adv. Appl. Math. (IF 1.1) Pub Date : 2023-07-28 Ming-Jian Ding, Bao-Xuan Zhu
Many 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