Speaker：Zhicong Lin (Shandong University)

Time：2024-4-9, 10:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

The original motivation of this paper was to find the context-free grammar for the joint distribution of peaks and valleys on permutations. Although such attempt was unsuccessful, we can obtain noncommutative symmetric function identities for the joint distributions of several descent-based statistics, including peaks, valleys and even/odd descents, on permutations via Zhuang's generalized run theorem. Our results extend in a unified way several generating function formulae exist in the literature, including formulas of Carlitz--Scoville (1973, 1974), Stanley (1976), Zhuang (2017) and Pan--Zeng (2019, 2023). As applications of these generating function formulas, Wachs' involution and Foata--Strehl action on permutations, we also investigate the signed counting of even and odd descents, and of descents and peaks.

This talk is based on joint work with Yao Dong.