组合理论与算法研讨会手册-CTA2023-0418(1).pdf

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 1 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 2 会议日程会议报到：2023 年 4 月 21 日下午 2 点-6 点，南楼 204 2023 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 合影与茶歇組合、图论學在物理、化學、統計上的應 10:20-10:50 叶永南用 10:50-11:20 A multiple q-translation formula 刘治国 11:20-11:50 非交换基本超几何级数导引张之正 11:50-12:20 Kazhdan-Lusztig polynomials of complete graphs 杨立波 12:30-13:30 午餐（物科宾馆自助） 14:00-15:00 15:00-16:00 Analytic Aspects of Combinatorial Sequences I Analytic Aspects of Combinatorial Sequences II 16:00-16:20 16:20-16:50 16:50-17:20 王毅王毅茶歇 Modularity of Nahm Sums for the Tadpole Diagram The stability of multivariate polynomial sequences 17:20-17:50 Ehrhart Theory on Lattice Path Matroids 18：00-20：00 晚宴（物科宾馆） 3 王六权刘丽范久瑜 2023 年 4 月 23 日周日（南楼 204 会议室）时间 8:30-9:30 9:30-10:30 日程 Analytic Aspects of Combinatorial Sequences III Analytic Aspects of Combinatorial Sequences IV 10:30-10:50 10:50-11:20 11:20-11:50 演讲人王毅王毅茶歇 Equidistribution of set-valued statistics on standard Young tableaux and transversals On lattice paths and the Thue-Morse sequence 严慧芳傅士硕 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 16:50-17:20 17:20-17:50 18：00-20：00 Further q-supercongruences from a transformation of Rahman Some results and problems on nontrivial cross intersecting families 张俊郭军伟张华军晚餐（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 9:50-10:20 Abel 引理与 q-级数变换马欣荣 10:20-10:50 Generalized q-partial differential equations for q-3D hypergeometric polynomials and some applications 曹健 4 10:50-11:20 Symmetries in parking functions, Dyck paths and trees 11:30-14:00 午餐 (物科宾馆) 14:00-17:00 自由讨论林志聪报告信息系列专题讲座题目 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：Analytic aspects of combinatorial 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. The talk consists of four parts. 1. Analytic aspects of combinatorial sequences---from the viewpoint of total positivity. 2. Unimodal, log-concave and Polya frequency sequences. 3. Log-convexity of combinatorial sequences. 4. Catalan-like numbers, log-convex and Stieltjes moment sequences. 5 邀请学术报告题目 1：組合、图论學在物理、化學、統計上的應用报告人：叶永南教授（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 2：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-translation 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 3：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。 6 题目 4：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 Kazhdan–Lusztig polynomials of complete graphs. In particular, they confirm a conjecture of Elias, Proudfoot and Wakeﬁeld on the top coefficients of Kazhdan–Lusztig polynomials of complete graphs. In this talk we will show how to determine the top coefficients of inverse Kazhdan–Lusztig polynomials of complete graphs based on Ferroni and Larson's work. 题目 5： 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 the 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 modular 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. 7 题目 6：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 polynomials, 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 position property of multivariate matching polynomials. 题目 7：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. 8 题目 8：Equidistribution of set-valued statistics on standard Young tableaux and transversals 报告人：严慧芳教授（浙江师范大学）摘要： As a natural generalization of permutations, transversals of Young diagrams play an important role in the study of pattern-avoiding permutations. In this talk, , we are mainly concerned with the distribution of the peak set and the valley set on standard Young tableaux and pattern-avoiding transversals. 题目 9：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 that the diagonal of certain bivariate rational function is congruent to the Thue-Morse series modulo 2. 题目 10：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。 9 题目 11： 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 quadratic 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 related conjectures on supercongruences and q-supercongruences. 题目 12：Some results and problems on nontrivial cross intersecting families 报告人：张华军教授（绍兴文理学院）摘要： 10 题目 13：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 new and general transformations with sixteen parameters and bases via Abel's 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 Rahman's quadratic,cubic, and quartic transformations. Furthermore, 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. This talk is based on joint work with Jianan Xu. 题目 14：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 investigation 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 addition, we generalize (q, c)-derivative operator of Zhang [Adv. Appl. Math. 121(2020), 102081, 23pp.] and (q, λ)-derivative operator of Yang 11 [Ramanujan J. 2022, https://doi.org/10.1007/s11139-022-00617-w.] and give some applications. Moreover, we define the generalized homogeneous Rogers--Szegöpolynomial and Stieltjes—Wigert 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 generalize some results of Ismail and Zhang. 题目 15：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 in Parking functions, Dyck paths and trees. This talk is based on my recent joint work with Yang Li and Tongyuan Zhao. 12