报告题目1：q-Supercongruences from Jackson's 8φ7 summation and Watson's 8φ7 transformation
报告人：魏传安教授，海南医科大学
报告时间：2024年11月8日（周五） 9:30-11:30
报告地点：20-200
摘要：q-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of Jackson's 8φ7 summation, Watson's 8φ7 transformation, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials. More concretely, we give a q-analogue of a nice formula due to Long and Ramakrishna [Adv. Math. 290(2016), 773–808] and two q-supercongruences involving double series.
报告人简介：魏传安，教授，博士毕业于上海师范大学，现任职于海南医科大学信息学院，从事超几何级数，基本超几何级数和q-同余式的研究，主持国家自然科学基金3项，在Journal of Combinatorial Theory, Series A, Advances in Applied Mathematics, Proceedings of the American Mathematical Society等期刊发表SCI论文50余篇。
报告题目2：Bijections in weakly increasing trees via binary trees
报告人：林志聪教授，山东大学
报告时间：2024年11月11日（周一） 14:30-17:00
报告地点：20-200
摘要：As a unification of increasing trees and plane trees, the weakly increasing trees labeled by a multiset was introduced by Lin-Ma-Ma-Zhou in 2021. Motived by some symmetries in plane trees proved recently by Dong, Du, Ji and Zhang, we construct four bijections on weakly increasing trees in the same flavor via switching the role of left child and right child of some specified nodes in their corresponding binary trees. Consequently, bijective proofs of the aforementioned symmetries found by Dong et al. and a non-recursive construction of a bijection on plane trees of Deutsch are provided. Applications of some symmetries in weakly increasing trees to permutation patterns and statistics will also be discussed.
报告人简介：林志聪，山东大学数学与交叉科学研究中心教授。主要从事计数组合学的研究，先后主持国家自然科学基金4项，在J. Combin. Theory Ser. A、Combinatorica等权威期刊发表SCI学术论文40余篇。任中国数学会计算机数学专业委员会委员和中国运筹学会图论组合分会青年理事。
报告题目3：r-Euler-Mahonian statistics on permutations
报告人：刘绍华博士，广东财经大学
报告时间：2024年11月11日（周一） 14:30-17:00
报告地点：20-200
摘要：In this talk, we prove that the pairs of permutation statistics (rdes, rmaj) and (rexc, rden) are equidistributed, where rmaj denotes the r-major index defined by Don Rawlings and rden denotes the r-Denert’s statistic defined by Guo-Niu Han. When r=1, our result reduces to the equidistribution of (des, maj) and (exc, den), which was conjectured by Denert in 1990 and proved that same year by Foata and Zeilberger. We call a pair of permutation statistics that is equidistributed with (rdes, rmaj) or (rexc, rden) an r-Euler-Mahonian statistic, which reduces to the classical Euler-Mahonian statistic when r = 1. We also introduce the permutation statistics desr, excr, majr, and denr. We prove that (desr, majr) is r-Euler-Mahonian and conjecture that (excr, denr) is r-Euler-Mahonian.
报告人简介： 刘绍华，广东财经大学讲师，2020年博士毕业于天津大学应用数学中心。主要研究计数组合学，特别是排列统计量。目前已取得多项研究成果，发表于J. Comb. Theory, Ser. A，Adv. Appl. Math，Eur. J. Comb. 等组合数学领域权威刊物。目前主持国家自然科学基金青年项目一项。