日程安排

5.17日上午8:00-11:30 学术报告 (地点：曲阜师范大学新葡萄8883官网AMG304会议室)
时间	主持人	报告人	题目
9:00-9:10	刘丽	开幕式
9:10-10:10	苏循团	王毅	Matchings and chains partitions in graded posets
10:10-10:30	茶歇
10:30-11:30	王毅	祝宝宣	Total positivity from exponential Riordan arrays
11:30-15:00	午餐
5.17日下午15:00-17:50 学术报告 (地点：曲阜师范大学新葡萄8883官网AMG304会议室)
15:00-15:30	祝宝宣	牟丽丽	Real rooted polynomials and f-polynomials of simplicial complexes
15:30-16:00	牟丽丽	梁胡义乐	Analytic properties of combinatorial sequences
16:00-16:20	茶歇
16:20-16:50	梁胡义乐	刘冠吾	Partitioning a triangle-free planar graph in to a forest and a forest of maximum degree one
16:50-17:20	刘冠吾	李冠儒	Clar covering polynomials with only real zeros
17:20-17:50	李冠儒	王亚玲	Analytic aspects of (generalized) central trinomial coefficients
18:00-20:00	晚餐
5.18日上午8:00-11:30 学术报告 (地点：曲阜师范大学新葡萄8883官网AMG304会议室)
9:00-9:30	王亚玲	陈曦	Combinatorics of the Delannoy lattice
9:30-10:00	陈曦	郑赛男	Eigenvalue inequalities for Hermitian matrices and totally positive matrices
10:00-10:30	郑赛男	毛建玺	Polya frequency sequence VS Stieltjes moment sequence
10:30-10:50	茶歇
10:50-11:20	毛建玺	裴艳妮	Log-convexity of Apéry-like numbers
11:20-11:50	裴艳妮	丁明健	Symmetric decompositions and s-Eulerian polynomials
11:50-14:30	午餐
5.18日下午15:00-17:30 自由讨论 (地点：曲阜师范大学新葡萄8883官网AMG304会议室)
15:00-17:30	自由讨论、离会

报告题目和摘要

报告题目：Matchings and chains partitions in graded posets

报告人：王毅   大连理工大学

报告摘要：Matchings and chain partitions play an important role in the extremal theory of posets. In this talk, we will give a short survey about various matchings and chain partitions in graded posets, with emphasis on the connection between these properties and the Sperner properties. We will also discuss some related open problems and conjectures.

报告题目：Total positivity from exponential Riordan arrays

报告人：祝宝宣   江苏师范大学

报告摘要：矩阵的全正性是数学中的一个强有力的工具，在数学的多个分支中有着重要的应用。组合学中的指数型Riordan阵起着统一性的作用，在本次报告中，我们将从指数型Riordan阵来介绍组合学中的一些全正性结果。

报告题目：Real rooted polynomials and f-polynomials of simplicial complexes

报告人：牟丽丽   江苏师范大学

报告摘要：Bell and Skandera conjecture that the real rootedness of a polynomial with positive integer coefficients implies that there is a simplicial complex $\Delta$ for which the coefficient is the number of $i$-dimensional faces of $\Delta$, or in other word the polynomial is the f-polynomial of a simplicial complex $\Delta$. We develop a new approach and collect further evidence for a positive answer to the question.

报告题目：Analytic properties of combinatorial sequences

报告人：梁胡义乐   内蒙古师范大学

报告摘要：In this talk, we will report some developments in analytic properties of combinatorial sequences. These properties include unimodality, log-concavity, log-convexity, Polya Frequency, Stieltjes moment properties, total positivity of matrices and polynomials with only real zeros. They often arise in Combinatorics and Analysis, Algebra and Geometry, Probability and Statistics, and so on.

报告题目：Partitioning a triangle-free planar graph in to a forest and a forest of maximum degree one

报告人：刘冠吾   山东理工大学

报告摘要：Kawarabayashi and Thomassen conjectured that perhaps the vertex-set of every triangle-free planar graph can be partitioned into a set that induces an independent set and a set that induces a forest. Dross, Montassier and Pinlou then asked the same question. In this paper, we prove that the vertex-set of every triangle-free planar graph can be partitioned into a set that induces a forest with maximum degree at most one and a set that induces a forest, which improves a result of Feghalir and Samal that the vertex set of every triangle-free planar graph can be partitioned into a set that induces a forest and a set that induces a forest with maximum degree at most 3.

报告题目：Clar covering polynomials with only real zeros

报告人：李冠儒   内蒙古民族大学

报告摘要：We present some examples of hexagonal systems whose Clar covering polynomials have only real zeros, and show that all real zeros of Clar covering polynomials are dense in the interval .

报告题目：Analytic aspects of (generalized) central trinomial coefficients

报告人：王亚玲   山西师范大学

报告摘要：The generalized central trinomial coefficients are common generalizations of many well-known combinatorial numbers, including the central binomial coefficient, the central Delannoy number, the central trinomial polynomial, the Narayana polynomial of type B, the Delannoy polynomial and the classical Legendre polynomial. The divisibility and congruence properties of the usual and generalized central trinomial coefficients have been extensively studied. In this talk we consider analytic properties of these numbers. This is joint work with Huyile Liang and Yi Wang.

报告题目：Combinatorics of the Delannoy lattice

报告人：陈曦   大连理工大学

报告摘要：Delannoy numbers are well-known combinatorial numbers in the enumeration of lattice paths. We define a graded poset whose Whitney numbers of the second kind are the Delannoy numbers, and show that this poset is a lattice, called the Delannoy lattice. In this talk, we introduce some combinatorial properties of the Delannoy lattice, including symmetric Boolean decompositions, supersolvability, Mobius functions, and zeta polynomials, etc.

报告题目：Eigenvalue inequalities for Hermitian matrices and totally positive matrices

报告人：郑赛男   东北财经大学

报告摘要：We present a characterization of eigenvalue inequalities between two Hermitian matrices by means of inertia indices. As applications, we give a common generalization of eigenvalue inequalities for (Hermitian) normalized Laplacian matrices of simple (signed, weighted, directed) graphs. Besides, it is well known that the eigenvalues of totally positive matrices are all real. We give a unified proof of the interlacing properties of eigenvalues of principle submatrices of totally positive matrices.

报告题目：Polya frequency sequence VS Stieltjes moment sequence

报告人：毛建玺   大连理工大学

报告摘要：In this talk we focus on two important sequences, namely the Polya frequency sequence and Stieltjes moment sequence. First we present a criterion for the case that the reciprocal of a Polya frequence sequence is a Stieltjes moment sequence. Both sequences are closely related to the complex decreasing zero sequence. Second we study the sum of complex decreasing zero sequence and give a partial answer to the question of Csordas et. al.

报告题目：Log-convexity of Apéry-like numbers

报告人：裴艳妮   三峡大学

报告摘要：Apéry-like numbers are the generalization of many well-known combinatorial numbers. There have been many investigates on their divisibility and congruence properties so far. In this talk, we discuss the log-convexity of Apéry-like numbers which satisfied the three-term recurrence.

报告题目：Symmetric decompositions and s-Eulerian polynomials

报告人：丁明健   大连理工大学

报告摘要：In this paper, we present a criterion for the self-interlacing property of $\bm{s}$-Eulerian polynomials, which partially affirms Schepers and Van Langenhoven's conjecture. As applications, we demonstrate that some $\bm{s}$-Eulerian polynomials possess this property, including the $1/k$-Eulerian polynomials, the $\ell$-Eulerian polynomials, and the $(1,4)$- and $(4,1)$-Eulerian polynomials. Besides, we provide an affirmative answer to Ding and Zhu's conjecture.