组合理论与算法研讨会.docx

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1、组合理论与算法研讨会会议手册2023年4月21日-24日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，北京会议信息时间：2023年4月21日-24日 （21日报到，地点数学院南楼204）地点：北京中关村东路55号中国科学院数学院南楼204会议室会议日程会议报到：2023年4月21日下午2点-6点，南楼2042023年4月22日周六学术报告（南楼204会议室）时间日程演讲人8:20-8:30签到8:30-8:40开幕8:40-8:50特邀学者讲话王军8:50-9:50置换与加法组合 I孙智伟9:50-10:20合影与茶歇10:20-10:50組合、图论學在物理、化學、統計上的應用叶永南10

2、:50-11:20A multiple q-translation formula刘治国11:20-11:50Abel引理与q-级数变换马欣荣11:50-12:20非交换基本超几何级数导引张之正12:30-13:30午餐（物科宾馆自助）14:00-15:00Analytic Aspects of Combinatorial Sequences I王毅15:00-16:00Analytic Aspects of Combinatorial Sequences II王毅16:00-16:20茶歇16:20-16:50Kazhdan-Lusztig polynomials of complete g

3、raphs杨立波16:50-17:20The stability of multivariate polynomial sequences刘丽17:20-17:50Ehrhart Theory on Lattice Path Matroids范久瑜18：00-20：00晚宴（物科宾馆）2023年4月23日周日（南楼204会议室）时间日程演讲人8:30-9:30Analytic Aspects of Combinatorial Sequences III王毅9:30-10:30Analytic Aspects of Combinatorial Sequences IV王毅10:30-10:50茶

4、歇 10:50-11:20Further Extensions of Haglund-Remmel-Wilson Identity严慧芳11:20-11:50On lattice paths and the Thue-Morse sequence傅士硕12:00-13:30午餐（物科宾馆自助）14:00-15:00置换与加法组合 II孙智伟15:00-16:00置换与加法组合 III孙智伟16:00-16:20茶歇16:20-16:50完全对称多项式零点的新下界 张俊16:50-17:20Further q-supercongruences from a transformation of R

5、ahman 郭军伟17:20-17:50On a conjecture of Tokushige for cross-t-intersecting families 张华军18：00-20：00晚餐（物科宾馆）2023年4月24日周一（南楼204会议室）时间日程演讲人8:30-9:30置换与加法组合 IV孙智伟9:30-9:50茶歇9:50-10:20Modularity of Nahm Sums for the Tadpole Diagram王六权10:20-10:50Generalized q-partial differential equations for q-3D hypergeo

6、metric polynomials and some applications曹健10:50-11:20Symmetries in parking functions, Dyck paths and trees林志聪11:30-14:00午餐 (物科宾馆)14:00-17:00自由讨论报告信息题目1：置换与加法组合报告人：孙智伟 教授（南京大学）摘要： 与Abel群加法结构有关的加法组合是组合和数论的交叉领域，国际上这方面的研究十分活跃。本课程讨论有关的置换与和集问题，介绍这方面的已有结果与研究方法， 还将提及一些未解决问题。题目2：組合、图论學在物理、化學、統計上的應用报告人：叶永南 教授

7、（温州大学）摘要： 在這個演講裏。我將用淺顯的語言簡單介紹過去我用組合、圖論在物理、化學、統計等跨學科領域的一些應用。题目3：A multiple q-translation formula报告人：刘治国 教授（华东师范大学）摘要： In this talk, we shall introduce a multiple q-exponential differential operational identity for the analytic functions in several variables, which can be regarded as a multiple q-tran

8、slation formula. This multiple q-translation formula is a fundamental result and play a pivotal role in q-mathematics. Using this formula, we can easily recover many classical conclusions in q-mathematics and derive some new q-formulas.题目4：Abel引理与q-级数变换报告人：马欣荣 教授（苏州大学）摘要： This talk is about three ne

9、w and general transformations with sixteen parameters and bases via Abels lemma on summation by parts. As their applications, we will exhibit some new transformations of basic hypergeometric series. Among include some new results of Gasper and Rahmans quadratic,cubic, and quartic transformations. Fu

10、rthermore, we put forward the so-called R,S-type transformation with arbitrary degree to unify such multibasic transformations. Some special R,S-type transformations are presented.题目5：非交换基本超几何级数导引报告人： 张之正 教授（洛阳师范学院）摘要：在本报告中，将从Gauss非交换二项式定理出发，介绍一般非交换基本超几何级数的基本概念及基本结果。题目6：Analytic aspects of combinato

11、rial sequences报告人：王毅 教授（大连理工大学）摘要： In this talk, we discuss some analytic properties of combinatorial sequences.题目7：Kazhdan-Lusztig polynomials of complete graphs报告人：杨立波 教授（南开大学）摘要： Recently, Luis Ferroni and Matt Larson provide a combinatorial interpretation of KazhdanLusztig polynomials of complet

12、e graphs. In particular, they confirm a conjecture of Elias, Proudfoot and Wakeeld on the top coefficients of KazhdanLusztig polynomials of complete graphs. In this talk we will show how to determine the top coefficients of inverse KazhdanLusztig polynomials of complete graphs based on Ferroni and L

13、arsons work.题目8：A unified approach to multivariate polynomial sequences with real stability报告人：刘丽 教授（曲阜师范大学）摘要： We give some new sufficient conditions for a sequence of multivariate polynomials to be real stable. As applications, we obtain the real stability of many important multivariate polynomial

14、s, such as multivariate Eulerian polynomials, multivariate Bell polynomials and multivariate polynomials over Stirling permutations in a unified manner. And we also show some new results, such as the real stability of multivariate polynomials over Jacobi-Stirling permutations, and the proper positio

15、n property of multivariate matching polynomials.题目9：Ehrhart Theory on Lattice Path Matroids报告人：范久瑜 副教授（四川大学）摘要： We will give a survey of the Ehrhart theory of lattice path maroids and report our recent progress on this topic.题目10：Further Extensions of Haglund-Remmel-Wilson Identity报告人：严慧芳 教授（浙江师范大学）

16、摘要： MacMahons equidistribution theorem states that the permutation statistics inversion number and major index are equidistributed. In 2015, Remmel and Wilson proved a conjectured identity of Haglund which is an extension of MacMahons equidistribution theorem to ordered set partitions. Recently, Liu

17、 extended this identity to k-Stirling permutations and posed a conjecture concerning an ascent analogue of his extension. In this talk, we shall present a combinatorial proof of this conjecture. Furthermore, we derive an analogous result for another maj- like statisticintroduced by Liu. This talk is

18、 based on joint work with Sha Ling, Lihong Yang and Robin D.P. Zhou. 题目11：On lattice paths and the Thue-Morse sequence报告人：傅士硕 教授（重庆大学）摘要： In answering a question of Berstel, Lauve, Reutenauer, and Saliola, we present a combinatorial argument basing on the symmetry of certain lattice paths to explain

19、 that the diagonal of certain bivariate rational function is congruent to the Thue-Morse series modulo 2.题目12：完全对称多项式零点的新下界报告人：张俊 教授（首都师范大学）摘要： 在报告中，我们介绍最新的关于完全对称多项式零点个数的下界，该下界大大改进了已有的下界。该工作是与万大庆教授合作。题目13： Further q-supercongruences from a transformation of Rahman报告人：郭军伟 教授（淮阴师范学院）摘要： Employing a qu

20、adratic transformation formula of Rahman and the method of creative microscoping (introduced by the author and Zudilin in 2019), we provide some new q-supercongruences for truncated basic hypergeometric series. In particular, we confirm two recent conjectures of Liu and Wang. We also propose some re

21、lated conjectures on supercongruences and q-supercongruences.题目14：On a conjecture of Tokushige for cross-t-intersecting families 报告人：张华军 教授（绍兴文理学院）摘要： Two families of sets A and B are called cross-t-intersecting if ABt for all AA, BB. In this talk, we will prove that for all kt3 and nt+1k-t+1, if A,

22、Bnk are cross-t-intersecting, then ABn-tk-t2, equality holds if and only if A and B are the same maximum t-intersecting family of nk. This confirms a conjecture of Tokushige for t3.题目15：Modularity of Nahm Sums for the Tadpole Diagram报告人：王六权 教授（武汉大学）摘要： We prove Rogers-Ramanujan type identities for t

23、he Nahm sums associated with the tadpole Cartan matrix of rank 3. These identities reveal the modularity of these sums, and thereby we confirm a conjecture of Calinescu, Milas and Penn in this case. We show that these Nahm sums together with some shifted sums can be combined into a vector-valued mod

24、ular function on the full modular group. We also present some conjectures for a general rank. This talk is based on a joint work with Antun Milas.题目16：Generalized q-partial differential equations for q-3D hypergeometric polynomials and some applications报告人：曹健 教授（杭州师范大学）摘要： In this talk, our investig

25、ation is focusing on q-analogue complex Hermite polynomials, which were motivated by Ismail and Zhang Adv. Appl. Math. 80(2016), 70 -92. and Trans. Amer. Math. Soc. 369(2017), 6779 -6821. We give a new pair of q-3D Hermite polynomials and their corresponding q-partial differential equations. In addi

26、tion, we generalize q,c-derivative operator of Zhang Adv. Appl. Math. 121(2020), 102081, 23pp. and q,-derivative operator of Yang Ramanujan J. 2022, https:/doi.org/10.1007/s11139-022-00617-w. and give some applications. Moreover, we define the generalized homogeneous Rogers-Szeg polynomial and Stiel

27、tjesWigert polynomial involving two parameters in the binomial coefficient and find their corresponding q-partial differential equations. Finally, we define generalized q-3D Hermite polynomials with double binomial coefficients, find their corresponding q-partial differential equations and generaliz

28、e some results of Ismail and Zhang.题目17：Symmetries in parking functions, Dyck paths and trees报告人：林志聪 教授（山东大学）摘要： I will talk about some bijective proofs of several symmetries arising inParking functions, Dyck paths and trees. This talk is based on my recent joint work with Yang Li and Tongyuan Zhao.14