报告人：Sergey Kitaev 教授（University of Strathclyde, UK）

时间：2026年05月13日 09:30-

地址：数统学院LD718

个人网站：https://spider-v.science.strath.ac.uk/sergey.kitaev/index.html

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.

邀请人：傅士硕