3月25日
8：00-11：30 学术报告（地点：威廉希尔中文网站304会议室）
时间	主持人	报告人	题目
8：00-8：10	刘丽	开幕式
8：10-8：40	苗正科	孙智伟 （南京大学）	Determinants involving second-order recurrences
8：40-9：10	王军	马欣荣 （苏州大学）	双边超几何级数Psi22求和公式 的存在性
9：10-9：40	侯庆虎	辛国策 （首都师范大学）	A combinatorial approach to Frobenius numbers of some special sequences
9：40-10：00	茶歇
10：00-10：30	李雨生	杨立波 （南开大学）	Some conjectures on q-log-concavity
10：30-11：00	张之正	王岁杰 （湖南大学）	K-adjoint arrangement (超平面配置的k-伴随）
11：00-11：30	王毅	梁胡义乐 （内蒙古师范大学）	Analytic aspects of (generalized) central trinomial coefficients
14:00-17:10学术报告 （地点：威廉希尔中文网站304会议室）
14：00-14：30	严慧芳	郭军伟 （淮阴师范学院）	New q-analogues of Van Hamme’s (E.2) supercongruence and of a super- congruence by Swisher
14：30-15：00	陈绍示	潘颢 （南京财经大学）	关于q-Delannoy数的Lucas型同余式
15：00-15：30	范久瑜	傅士硕 （重庆大学）	Combinatorial perspectives on some double-sum Rogers-Ramanujan type identities
15：30-15：50	茶歇
15：50-16：20	林志聪	张华军 （绍兴文理学院）	On a conjecture of Tokushige for cross- t-intersecting families
16：20-16：50	魏传安	李冠儒 （内蒙古民族大学）	Analytic properties of sextet polynomial of hexagonal systems
16：50-17：00	苏循团	闭幕式
17：00-17：10	合  影
3月26日
8：00-11：30	自由讨论
14：00-	离会

 

报告摘要

 

Combinatorial perspectives on some double-sum Rogers-Ramanujan type identities

傅士硕   重庆大学

  We give Gordon type partition theoretical interpretations for the series sides of four double-sum identities of Rogers-Ramanujan type. Two of them are of index (1,2) and the other two of index (1,3). As a result of our combinatorial approach, we are able to construct direct bijective proofs to the two identities of index (1,2), which were previously established by Cao and Wang using an integral method.

 

New q-analogues of Van Hamme's (E.2) supercongruence and of a supercongruence by Swisher

郭军伟   淮阴师范学院

In this talk, a couple of $q$-supercongruences for truncated basic hypergeometric series are proved, most of them modulo the cube of a cyclotomic polynomial. One of these results is a new $q$-analogue of the (E.2) supercongruence by Van Hamme, another one is a new $q$-analogue of a supercongruence by Swisher, while the other results are closely related $q$-supercongruences. The proofs make use of special cases of a very-well-poised ${}_6\phi_5$ summation. In addition, the proofs utilize the method of creative microscoping (which is a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.

 

 

 

 

Analytic aspects of (generalized) central trinomial coefficients

梁胡义乐    内蒙古师范大学

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. There have been quite a few papers concerned with the divisibility and congruence of generalized central trinomial coefficients. In this talk, we will introduce some analytic properties of (generalized) central trinomial coefficients. This is joint work with Yaling Wang and Yi Wang.

 

 

 

 

Analytic properties of sextet polynomial of hexagonal systems

李冠儒    内蒙古民族大学

The sextet polynomial is the first genuine mathematical object introduced within the aromatic sextet theory. In this talk, we investigate analytic properties of sextet polynomials of hexagonal systems, especially for the pyrene chains and parallelogram chain. For general hexagonal systems, we also show the distribution of real zeros of sextet polynomials.

 

 

 

 

双边超几何级数Psi22求和公式的存在性

马欣荣   苏州大学

利用差分法，报告人与合作者建立了Ramanujan psi11和Bailey psi66所满足的共同的递推关系，从而可以给出这两个重要的求和公式的初等证明. 但不能确定满足该递推关系的psi22 级数是否存在封闭的求和公式.报告人将汇报围绕这一问题所取得一些进展。

 

 

 

关于q-Delannoy数的Lucas型同余式

潘颢   南京财经大学

我们介绍一个关于q-Delannoy数的Lucas型同余式。证明的关键在于基于area统计量的组合解释以及针对Delannoy格路的群作用构造。

 

 

 

 

 

Determinants involving second-order recurrences

孙智伟   南京大学

 In this talk we introduce our recent results on determinants involving second-order recurrences (such as Fibonacci numbers and Lucas sequences), some of them are joint with the speaker’s graduate student Han Wang.

 

 

 

 

 

k-adjoint arrangement (超平面配置的k-伴随)

王岁杰   湖南大学

In this talk, we will introduce a recent work joint with Chengdong Zhao and Weikang Liang. In our paper, we introduce a new approach for constructing new hyperplane arrangements from the intersection lattice of a given hyperplane arrangement, called k-adjoint of a hyperplane arrangement,  which has connections or applications with the following objects.

(1) Extend the concept of adjoint of a hyperplane arrangement by Bixby and Coulard;

(2) Provide a combinatorial classification of all k-restrictions of a fixed hyperplane arrangement;

(3) Serve as a combinatorial Decomposition of Grassmannian,equivalent to both matroid statification

   and permuted Schubert decomposition;

(4) Present the anti-continuity property of some combinatorial invariants for all k-restrictions of a fixed hyperplane arrangement.

 

 

 

 

 

A combinatorial approach to Frobenius numbers of some special sequences

辛国策   首都师范大学

Let $A=(a_1, a_2, ..., a_n)$ be relative prime positive integers with $a_i\geq 2$. The Frobenius number $g(A)$ is the greatest integer not belonging to the set $\big\{ \sum_{i=1}^na_ix_i\ |x_i\in \mathbb{N}\big\}$. The general Frobenius problem includes the determination of $g(A)$ and the related Sylvester number $n(A)$ and Sylvester sum $s(A)$. We present a new approach to the Frobenius problem. Basically, we transform the problem into an easier optimization problem. If the new problem can be solved explicitly, then we will be able to obtain a formula of $g(A)$. We illustrate the idea by giving concise proofs of some existing formulas and finding some interesting new formulas of $g(A), n(A), s(A)$. Moreover, we find that MacMahon's partition analysis applies to give a new way of calculating $n(A), s(A)$ by using a rational function representation of a polynomial determined by $A$.

 

 

 

 

Some conjectures on q-log-concavity

杨立波   南开大学

In recent years the log-concavity of matroid invariants has received considerable research attention. One of the outstanding conjectures states that all matroid Kazhdan-Lusztig polynomials are log-concave. In this talk I will present some conjectures on $q$-log-concavity arising from the study of log-concavity of the Kazhdan-Lusztig polynomials of $q$-uniform matroids.

 

 

 

 

 

On a conjecture of Tokushige for cross-t-intersecting families

张华军   绍兴文理学院

Two families of sets $\mathcal{A}$ and $\mathcal{B}$ are called cross-$t$-intersecting if $|A\cap B|\ge t$ for all $A\in \mathcal{A}$, $B\in \mathcal{B}$. In this talk, we will prove that for all $k\geqt\geq3$ and $n\get+1)(k-t+1)$, if $\mathcal{A},\mathcal{B}\subseteq{\binom{[n]{k}}$ ar

e cross-$t$-intersecting, then $|\mathcal{A}||\mathcal{B}|\le{\binom{n-t}{k-t}}^2$, equality holds if and only if $\mathcal{A}$ and $\mathcal{B}$ are the same maximum $t$-intersecting family of $

\binom{[n]}{k}$. This confirms a conjecture of Tokushige for $t\ge 3$.