会议主题：

此次“组合理论与算法云端论坛”是由中国科学院数学与系统科学研究院数学机械化重点实验室与数学院青促会小组联合主办，中国数学会计算机数学专业委员会协办的线上会议, 旨在为国内组合理论与算法领域的学术研讨提供平台，促进相关领域专家学者的交流与合作。

 

会议时间：2022年12月10日—11日

会议信息：腾讯会议ID: 359 8076 8000 密码：202212 

 

会议联系人：

陈绍示 schen@amss.ac.cn

马平川 pcma@amss.ac.cn

李秀云 lixiuyun@amss.ac.cn

王艺森 wangyisen@amss.ac.cn

 

 

 

 

会议日程

2022年12月10日（周六）

 

2022年12月11日（周日）

 

 

报告1：王国庆(天津工业大学)

报告题目：代数结构上的零和问题

【摘要】 零和是组合数论的一个分支，其主要研究内容是群元素赋权下组合结构（包含集合、重集、图与超图等）中具有给定加法性质组合子结构的存在性、 结构的刻画、 以及相应的其他组合性质的探讨。零和研究起源于上世纪60年代Davenport常量的提出以及Erdos-Ginzburg-Ziv定理。本报告将介绍零和在群上的研究问题与发展，并结合报告人近期的一些研究工作，在半群和环等代数结构上对零和进行探讨。

 

【报告人简介】 王国庆，教授，博士生导师，任职于天津工业大学数学科学学院。2008年博士毕业于大连理工大学基础数学专业，主要从事组合数论与堆垒代数方向的研究工作，主要研究兴趣是群、半群、环等代数结构上序列相关的堆垒问题。在 《Journal of Combinatorial Theory A》、 《Journal of Number Theory》、《Acta Arithematica》、 《Journal of Graph Theory》、 《Communications in Algebra》、 《Semigroup Forum》 等杂志发表论文三十余篇。主持完成国家自然科学青年基金项目一项、主持在研国家自然科学基金面上项目一项，2015年获天津数学会青年学术一等奖。

 

报告2：靳宇(厦门大学)

报告题目：Tree-like graphs and Brownian excursion: from discrete to continuous

【摘要】 In this talk, I will start with a classical kind of tree-like graphs: the graphs with a bounded width and present well-known results from the enumerative aspect. Then I will describe the space of random tree-like graphs and establish a scaling limit of such graphs to the Brownian Continuum Random Tree (BCRT). The transition from discrete to continuous is achieved by combining different tools and methods such as bijections, generating functions, Boltzmann sampler and size-biased Galton-Watson trees. This talk requires no prior knowledge.

 

【报告人简介】 靳宇，厦门大学教授，2005年西南大学本科毕业，2010年南开大学博士毕业。在德国凯泽斯劳滕大学，奥地利维也纳科技大学和维也纳大学从事博士后研究。主要从事组合计数和解析组合方向的研究工作。

 

报告3：徐策(安徽师范大学)

报告题目：Multiple Mixed Values

【摘要】 In this talk we will consider a variant of multiple zeta values (MZVs) of level two, called multiple mixed values (MMVs), which forms a subspace of the space of alternating MZVs. This variant includes both Hoffman's multiple t-values and Kaneko-Tsumura's multiple T-values as special cases. We will explore their properties similar to ordinary MZVs such as the duality, integral shuffle and series stuffle relations. In the end, we compute the dimensions of a few interesting subspaces of MMVs for weight less than 13. This work is joint with J. Zhao.

 

【报告人简介】 徐策，硕士生导师，安徽师范大学数学与统计学院副教授。2020年博士毕业于厦门大学，同年加盟安徽师范大学数学与统计学院。曾在日本九州大学访学一年，师从Masanobu Kaneko教授，长期从事多重zeta值（Multiple zeta values, MZVs）及其相关变形的研究。主持国家自然科学基金，安徽省自然科学基金和安徽省教育厅高校项目各1项。在《Mathematische Zeitschrift》、《Journal of Algebra》、《Journal of Number Theory》等期刊发表论文40余篇。

 

报告4：熊欢(哈尔滨工业大学)

报告题目：On moments of sizes for random (n,dn±1)-core partitions with distinct parts

【摘要】 Amdeberhan's conjectures on the enumeration, the average size, and the largest size of (n,n+1)-core partitions with distinct parts have motivated many research on this topic. For example, Straub and Nath-Sellers obtained formulas for the numbers of (n,dn-1) and (n,dn+1)-core partitions with distinct parts, respectively. Let X_s,t be the size of a uniform random (s,t)-core partition with distinct parts when s and t are coprime to each other. Some explicit formulas for the k-th moments E[X_(n,n+1)^k] and E[X_(2n+1,2n+3)^k] were given by Zaleski and Zeilberger when k is small. Zaleski also studied the expectation and higher moments of X_n,dn-1 and conjectured some polynomiality properties concerning them in arXiv:1702.05634. 

Motivated by the above works, we derive several polynomiality results and asymptotic formulas for the k-th moments of X_n,dn+1 and X_n,dn-1, by studying the beta sets of core partitions. In particular, we show that these k-th moments are asymptotically some polynomials of n with degrees at most 2k, when d is given and n tends to infinity. Moreover, when d=1, we derive that the k-th moment E[X_(n,n+1)^k] of X_(n,n+1) is asymptotically equal to (n^2 \/10)^k when n tends to infinity. The explicit formulas for the expectations E[X_(n,dn+1) ] and E[X_(n,dn-1) ] are also given. The (n,dn-1)-core case in our results proves several conjectures of Zaleski on the polynomiality of the expectation and higher moments of X_n,dn-1.

 

【报告人简介】 熊欢，哈尔滨工业大学数学研究院教授，博士生导师。研究方向为组合数学和机器学习，特别是通过引入并研究分拆差分算子给出了随机整数分拆的若干渐进结果。在TPAMI, JCTA, Sci. China Math., ICML, NeurIPS等国际知名期刊和会议发表论文三十余篇。主持或参与瑞士国家自然科学基金、法国国家科研中心的多项研究项目。

 

报告5：杜庆丹(河北师范大学)

报告题目：Andrews-Beck type congruences for k-colored partitions

【摘要】 Beck introduced a new partition statistic which denotes the total number of parts of all partitions concerning Dyson's rank. Andrews proved two Andrews-Beck type congruences which were conjectured by Beck. Lin, Peng and Toh considered this phenomenon in k-colored partitions with certain generalized crank, and proved several Andrews-Beck type congruences. Moreover, they posed eight conjectural congruences. In this talk, we present a general strategy that will provide a unified treatment of the Andrews-Beck type congruences for k-colored partitions, including all of the above. This is a joint work with Dazhao Tang.

 

【报告人简介】 杜庆丹，河北师范大学数学科学学院讲师，主要研究符号计算和组合数学，在《Annals of Combinatorics》、《Journal of Symbolic Computation》、《Ramanujan Journal》等期刊上发表论文，主持国家自然科学青年基金和河北省青年科学基金各1项。

 

报告6：汪荣华(天津工业大学)

报告题目：Polynomial Reduction and -Series

【摘要】 We will introduce the theory and classical algorithms in the mechanical proofs of combinatorial identities, among which the reduction based algorithms have gained the most attention. In this talk, we will also introduce the (q-)polynomial reduction and applications in the automatically proof of  -series and congruences.

 

【报告人简介】 汪荣华，副教授，硕士生导师，奥地利林茨大学博士后。主要研究方向为组合数学与计算机代数，在《Advances in Applied Mathematics》、《Journal of Number Theory》、《Journal of Symbolic Computation》等期刊发表论文十余篇，主持在研国家青年基金1项，主持完成天津市青年基金1项，主持完成中科院数学机械化重点实验室开放课题1项，参与完成国家优青项目一项、面上项目2项。中国数学会计算机数学专业委员会委员，天津市“131”创新型人才培养工程第三层次人才，天津市“青年后备人才”。

 

报告7：吴耀琨(上海交通大学)

报告题目：Inclusion matrix

【摘要】 The zeta function of a Boolean algebra is often known as an inclusion matrix.  In this expository talk, we report some nice properties of the inclusion matrix and its various submatrices. This talk is accessible to a student knowing some basic linear algebra.

 

【报告人简介】 吴耀琨，上海交大博士毕业后留校工作至今。在上海交大任教期间努力借助各种上课机会认真学习一些简单有趣的数学，并且与学生一起将一些教学体会写成研究文章。

 

报告8：赵承东(中南大学)

报告题目：A-Schubert decomposition, matroid stratification and k-dimensional restrictions

【摘要】 Let A be a hyperplane arrangement in . We are concerned with a fundamental problem that how to give a combinatorial classification of all the k-dimensional restrictions of A. To this end, we introduce k-adjoint of A. In this talk, we also link k-dimensional restrictions with three different Grassmannian decompositions and give some applications of k-adjoint in combinatorial invariants.

This work is joint with Weikang Liang（梁卫康） and Suijie Wang（王岁杰）.

 

【报告人简介】 赵承东，中南大学数学与统计学院讲师，2015年本科毕业于四川大学，2020年博士毕业于南开大学组合数学中心，师从陈永川院士，主要研究代数组合。