17 citations · 35 across the 20 of their papers we have counts for
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Total positivity from a kind of lattice paths
Yu-Jie Cui, Bao-Xuan Zhu
Total positivity of matrices is deeply studied and plays an important role in various branches of mathematics. The main purpose of this paper is to study total positivity of a matr…
Coefficientwise Hankel-total positivity of the row-generating polynomials for the output matrices of certain production matrices
Bao-Xuan Zhu
Total positivity of matrices is deeply studied and plays an important role in various branches of mathematics. The aim of this paper is to study the criteria for coefficientwise Ha…
Stability of combinatorial polynomials and its applications
Ming-Jian Ding, Bao-Xuan Zhu
The aim of this paper is to make a systematical study on the stability of polynomials in combinatorics. Applying the characterizations of Borcea and Brändén concerning linear opera…
On a Stirling-Whitney-Riordan triangle
Bao-Xuan Zhu
Based on the Stirling triangle of the second kind, the Whitney triangle of the second kind and one triangle of Riordan, we study a Stirling-Whitney-Riordan triangle $[T_{n,k}]_{n,k…
A unified approach to combinatorial triangles: a generalized Eulerian polynomial
Bao-Xuan Zhu
Motivated by the classical Eulerian number, descent and excedance numbers in the hyperoctahedral groups, an triangular array from staircase tableaux and so on, we study a triangula…
Stieltjes moment properties and continued fractions from combinatorial triangles
Bao-Xuan Zhu
Many combinatorial numbers can be placed in the following generalized triangular array satisfying the recurrence relation: \begin{equation*} T_{n,k}=λ(a_0n+a…
Total positivity from the exponential Riordan arrays
Bao-Xuan Zhu
Log-concavity and almost log-convexity of the cycle index polynomials were proved by Bender and Canfield [J. Combin. Theory Ser. A 74 (1996)]. Schirmacher [J. Combin. Theory Ser. A…
Positivity of iterated sequences of polynomials
Bao-Xuan Zhu
In this paper, we present some criteria for the --log-convexity and --log-convexity of combinatorial sequences, which can be regarded as the first column of certain inf…
Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes--Rogers and Thron--Rogers polynomials, with coefficientwise Hankel-total positivity
Mathias Pétréolle, Alan D. Sokal, Bao-Xuan Zhu
We define an infinite sequence of generalizations, parametrized by an integer , of the Stieltjes--Rogers and Thron--Rogers polynomials; they arise as the power-series expa…
Asymptotic normality of Laplacian coefficients of graphs
Yi Wang, Haixia Zhang, Baoxuan Zhu
Let be a simple graph with vertices and let denote the Laplacian characteristic polynomial of . Then if the size is l…
Log-convex and Stieltjes moment sequences
Yi Wang, Bao-Xuan Zhu
We show that Stieltjes moment sequences are infinitely log-convex, which parallels a famous result that (finite) Pólya frequency sequences are infinitely log-concave. We introduce…
Context-free grammars for several polynomials associated with Eulerian polynomials
Shi-Mei Ma, Jun Ma, Yeong-Nan Yeh +1
In this paper, we present grammatical descriptions of several polynomials associated with Eulerian polynomials, including q-Eulerian polynomials, alternating run polynomials and de…
Hankel-type determinants for some combinatorial sequences
Bao-Xuan Zhu, Zhi-Wei Sun
In this paper we confirm several conjectures of Z.-W. Sun on Hankel-type determinants for some combinatorial sequences including Franel numbers, Domb numbers and Apéry numbers. For…
Linear transformations and strong -log-concavity for certain combinatorial triangle
Bao-Xuan Zhu
It is well-known that the binomial transformation preserves the log-concavity property and log-convexity property. Let be the binomial coefficients and $\binom{n…
Unimodality of the independence polynomials of some composite graphs
Bao-Xuan Zhu, Qinglin Lu
Let denote the independence polynomial of a graph . In this paper we study the unimodality properties of for some composite graphs . Given two graphs …
Strong q-log-convexity of the Eulerian polynomials of Coxeter groups
Lily Li Liu, Bao-Xuan Zhu
In this paper we prove the strong -log-convexity of the Eulerian polynomials of Coxeter groups using their exponential generating functions. Our proof is based on the theory of…
Operations of graphs and unimodality of independence polynomials
Bao-Xuan Zhu
Given two graphs and , assume that is a clique cover of and is a subset of . We introduce a new graph operation called th…
Higher order log-monotonicity of combinatorial sequences
Bao-Xuan Zhu
A sequence is called ratio log-convex in the sense that the ratio sequence is log-convex. Based on a three-term recurrence for…
Monotonicity and log-behavior of some functions related to the Euler Gamma function
Bao-Xuan Zhu
The aim of this paper is to develop analytic techniques to deal with certain monotonicity of combinatorial sequences. (1) A criterion for the monotonicity of the function $\sqrt[x]…
Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences
Yi Wang, Bao-Xuan Zhu
We develop techniques to deal with monotonicity of sequences z_{n+1}/z_n and \sqrt[n]{z_n}. A series of conjectures of Zhi-Wei Sun and of Amdeberhan et al. are verified in certain…