报告题目：Stable patterns and properties on permutations of multisets

报告人：Sergey Kitaev教授，英国思克莱德大学

报告时间：2026年4月20日（周一）9:00-12:00

报告地点：20-308

报告摘要：A property on permutations of multisets is stable if its corresponding generating function is symmetric, and a pattern is stable if the generating function for its distribution is symmetric. In other words, stability means invariance under permutations of multiplicities in multisets. For example, a property may behave identically on permutations of the multisets {1,1,2,2,2,3} and {1,1,1,2,3,3}.We show that the only stable classical patterns are those of length one or two. Moreover, we prove that all monotone consecutive patterns are stable and identify a large class of unstable consecutive patterns. These results are obtained bijectively. We conjecture that monotone patterns are the only stable consecutive patterns.As an application of the notion of stability, we derive recurrence relations for the descent distribution on permutations of multisets, yielding a generalization of Eulerian numbers.This is joint work with Shaoshi Chen and Hanqian Fang.

报告人简介：Sergey Kitaev，英国思克莱德大学理学院副院长、数学与统计学系教授。2003年博士毕业于瑞典哥德堡大学。主要研究组合数学、图论、代数、离散数学和形式语言理论等，完成《Patterns in permutations and words》和《Words and graphs》两本著作，多篇论文发表在J. Combin. Theory Ser. A，Adv in Appl. Math.，European J. Combin.等组合数学权威杂志上。目前担任Journal of Combinatorial Theory, Series A (JCTA) 和 Proceedings of the Edinburgh Mathematical Society (PEMS)杂志编委。

邀请人：离散数学研究所