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数学学科离散数学研究所学术报告(2021解析组合与计数组合系列报告会)

发布者:戴 情   发布时间:2021-10-21  浏览次数:164

报告一:

报告题目 Holonomic Polynomial Sequences I: Degree Growth

报告人 陈绍示 (中国科学院数学与系统科学研究院)

报告时间:1023日(周六),8:30-9:10

腾讯会议ID:   362 403 552

 摘要: A sequence $P_n(x)$ of polynomials in $x$ is holonomic (P-recursive) if it satisfies a linear recurrence with polynomial coefficients in $x$ and $n$. Many polynomial sequences from combinatorics, representation theory and number theory are shown to be holonomic. It is natural and fundamental to study the degree pattern of holonomic polynomial sequences. We will present a classification of the degree growth of such sequences and explain two applications related to combinatorial identities and exponential sums over finite fields respectively. This is a joint work with Jason P. Bell, Daqing Wan, Rong-Hua Wang and Hang Yin.

 

报告人简介:陈绍示, 现为中国科学院数学与系统科学研究院副研究员, 博士生导师。主要研究符号计算,计算微分代数与组合数学。2005年毕业于江苏大学信息与计算科学系。2011年中国科学院与法国巴黎综合理工学校联合培养博士毕业,曾先后在奥地利林茨大学、美国北卡罗来纳州立大学、加拿大菲尔兹数学研究所与滑铁卢大学从事博士后工作。在符号计算领域旗舰会议 ISSAC 发表论文16篇,以及Algebra and Number TheoryJournal of Symbolic ComputationJournal of Algebra, Journal of Combinatorial theory, Series A 等期刊发表论文 10 余篇。目前担任国际计算机协会 ACM SIGSAM 的秘书长与中国数学会计算机数学专业委员会秘书长,国际符号与代数计算年会ISSAC 指导委员会主席,以及担任《Annals of Combinatorics, Journal of Systems Science and Complexity》等学术期刊编委。曾获得第二届 “吴文俊计算机数学青年学者奖”与 第46届国际符号与代数计算年会“ISSAC2021杰出论文奖”。入选中国科学院第七届“陈景润未来之星”人才计划和中国科学院2018年度青年创新促进会会员。

 

报告二:

报告题目 Total positivity of matrices defined by linear recurrences

报告人 陈曦 (大连理工大学)

报告时间:1023日(周六),9:10-9:50

腾讯会议ID:   362 403 552

 摘要: A finite or infinite matrix with integer or real coefficients is called totally positive if all its minors are nonnegative. Such matrices have a wide variety of applications across pure and applied mathematics. In this talk, we exhibit a low-triangular matrix of polynomials in six indeterminates that appears empirically to be coefficientwise totally positive. We prove the coefficientwise total positivity of a special case of such matrices, which includes the reversed Stirling subset triangle.

报告人简介:陈曦,大连理工大学数学科学学院副教授、硕士生导师。2015年博士毕业于大连理工大学,2012-2013年赴美国密歇根州立大学联合培养一年,2019-2020年赴英国伦敦大学学院公派访问一年。主要研究组合矩阵的全正性和组合序列的解析性质,在European J. Combin., J. Algebraic Combin. 等期刊发表论文十余篇。主持国家自然科学基金青年基金一项。

 

报告三:

报告题目 Moment properties of combinatorial sequences

报告人 梁胡义乐 (内蒙古师范大学)

报告时间:1023日(周六),10:00-10:40

腾讯会议ID:   362 403 552

 摘要:  Stieltjes moment sequences and Hamburger moment sequences play an important role in different mathematical branches. In this talk, we will report some results for moment properties of combinatorial sequences.

报告人简介:梁胡义乐,女,博士研究生,讲师,硕士生导师,现任内蒙古数学学会理事。主持国家自然科学基金项目1 项、内蒙古自然科学基金项目 1 项、内蒙古教育厅项目 1 项。主要研究方向是组合数学,研究组合序列的moment性质、全正性等。

 

报告四:

报告题目 Pattern avoidance and lattice walks

报告人 林志聪  (山东大学数学与交叉科学研究中心)

报告时间:1023日(周六),10:40-11:20

腾讯会议ID:   362 403 552

 摘要:  I will present some intriguing connections between pattern avoiding permutations and lattice walks.

报告人简介:山东大学数学与交叉科学研究中心教授,2014年于法国里昂一大获得理学博士学位,主要从事计数组合学的研究,在《J. Combin. Theory Ser. A》、《Combinatorica》、《European J. Combin.》、《Proc. Amer. Math. Soc.》等多个学术刊物发表SCI学术论文30余篇。近期的研究兴趣主要集中在排列统计量及其相关组合结构上的双射和同分布问题。先后主持国家自然科学基金面上项目1项,青年基金1项。

 

报告五:

报告题目 ({M},i)-multiset Eulerian polynomials

报告人 马俊 (上海交通大学数学科学学院)

报告时间:1023日(周六),11:20-12:00

腾讯会议ID:   362 403 552

 摘要:  Denote by $\mathfrak{S}_{M,i}$  the set of multipermutations, in which the element in the first position is fixed as an integer $i$, on a multiset $M=\{1^{p_1},\ldots,n^{p_n}\}$. Let $A_{{M},i}(x,q)$ be the joint distribution polynomial of descents and major index of multipermutations in $\mathfrak{S}_{M,i}$. In this talk, we will first discuss a calculation formula for $A_{{M},i}(x,q)$.  $({M},i)$-multiset Eulerian polynomials $A_{M,i}(x)$ are the descent polynomials of multipermutations in $\mathfrak{S}_{M,i}$. We will show that $xA_{M,i}(x)$, $c_1A_{M,i}(x)+c_2A_{M,j}(x)$ and $c_1xA_{M,i}(x)+c_2A_{M,j}(x)$ have only real roots, where $c_1$ and $c_2$ are nonnegative real number, $i,j\in M$ and $i<j$. Use $[n]_k$ to denote the the multiset $\{1^k,2^k,\ldots,n^k\}$.  It is also shown that $A_{[n]_k,i}(x)$ is reciprocal with $A_{[n]_k,n-i+1}(x)$ for any $1\leq i\leq n$. We also prove that $A_{[n]_k,i}(x)+A_{[n]_k,n-i+1}(x)$ and $xA_{[n]_k,i}(x)+A_{[n]_k,n-i+1}(x)$ are $\gamma$-positive, and $A_{[n]_k,i}(x)$ is bi-$\gamma$-positive. Taking $k=1$, write $A_{[n]_k,i}(x)=A_{n,i}(x)$ for short. We give a combinatorial interpretation for $\gamma$-coefficients of $A_{n,i}(x)+A_{n,n-i+1}(x)$ for any $1\leq i\leq n$.

报告人简介:马俊,2006年从上海交通大学数学科学学院博士毕业,后2006年至2009年,在台北“中央研究院”数学所从事过为期三年的博士后研究工作,2010年到上海交通大学工作,现为上海交通大学数学科学学院副教授,主要研究组合设计与编码、代数组合、计数组合学及其应用等方面的问题,主持完成国家自然科学基金面上项目一项,研究成果发表在J. Combin. Theory Ser. A, Adv. Appl. Math., SIAM Discrete Math., Designs, Codes and Cryptography, Journal of Graph Theory等国际数学期刊。

 

报告六:

报告题目 Eulerian pairs and Hermite-Biehler pairs

报告人 马世美 (东北大学秦皇岛分校

报告时间:1023日(周六),14:00-14:40

腾讯会议ID:   362 403 552

 摘要:  In this talk, we discuss the definitions of Eulerian pair and Hermite-Biehler pair. We also characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems. This generalizes and unifies Hermite-Biehler decompositions of several enumerative polynomials, including up-down run polynomials for symmetric groups, alternating run polynomials for hyperoctahedral groups, flag descent polynomials for hyperoctahedral groups and flag ascent-plateau polynomials for Stirling permutations.

报告人简介:马世美,博士毕业于大连理工大学,现为东北大学秦皇岛分校副教授,长期围绕排列统计及其相关多项式展开研究。最近几年在文法理论和gamma正性问题上做出了较为系统的工作,部分论文发表在Journal of combinatorial theory, Series AEuropean journal of combinatorics等权威期刊上,目前主持国家自然科学基金面上项目1项。


报告七:

报告题目 On the unimodality of average edge cover polynomials

报告人 牟丽丽 (江苏师范大学)

报告时间:1023日(周六),14:40-15:20

腾讯会议ID:   362 403 552

 摘要:  The concept of the edge cover polynomial was first introduced by Akbari and Oboudi. It was shown to have some interesting properties and connect with many other well known polynomials associated with graphs. Noticing it is often of interest to study the average graph polynomials, we intended to observe the edge cover polynomials from this angle. Our stimulation also partly comes from some independent work on various kinds of average graph polynomials, especially the work of Brown et al. on average independence polynomials. Specifically, we show that the average edge cover polynomial of order n is reduced to the edge cover polynomial of complete graph K_n, based on which we conclude that the average edge cover polynomial of order n is unimodal and has at least n-3 non-real roots.

报告人简介:牟丽丽,2016年毕业于大连理工大学,江苏师范大学数学与统计学院副教授。硕士研究生导师,美国麻省理工学院(MIT)访问学者、英国伦敦大学学院(UCL)访问学者、台湾中央研究院访问学者。研究方向为组合数学。

 

报告八:

报告题目 The [k]-conflicting noncrossing partitions

报告人 苏循团 (曲阜师范大学)

报告时间:1023日(周六),15:30-16:10

腾讯会议ID:   362 403 552

 摘要:  The noncrossing partitions and their relatives have been extensively studied. In this talk,  we introduce a new family  of noncrossing partitions named as [k]-conflicting noncrossing partitions,  based upon our bijection between the ballot paths and the closed flows on forks. We will present the structural and enumerative properties of the [k]-conflicting noncrossing partitions.

报告人简介:苏循团,曲阜师范大学副教授,硕士生导师,博士毕业于大连理工大学,主要研究代数组合学中组合序列的单峰型性质及其应用。学术成果发表于Discrete Math., J. Math. Anal. Appl. 等期刊,主持过国家自然科学基金青年基金等多个项目。


报告九:

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)

报告时间:1023日(周六),16:10-16:50

腾讯会议ID:   362 403 552

 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.

报告人简介:郑赛男,东北财经大学讲师,硕士生导师。于201910月在大连理工大学数学科学学院获得博士学位。20159月至201610月在加州大学圣地亚哥分校(UCSD)应用数学系联合培养一年。研究方向为组合数学,主要研究兴趣包括组合计数、组合矩阵及组合多项式的解析性质。在组合数学领域主流期刊发表学术论文多篇,如《Advances in Applied Mathematics,Discrete Mathematics,Journal of Algebraic Combinatorics》等。主持国家自然科学基金青年基金项目及辽宁省教育厅科研基金项目。

邀请人:严慧芳