Cyclic descent extensions and distributions

Ron M. Adin, Victor Reiner, Sergi Elizalde, Yuval Roichman

Research output: Contribution to journalConference articlepeer-review

Abstract

The notion of descent set is classical both for permutations and for standard Young tableaux (SYT). Cellini introduced a natural notion of cyclic descent set for permutations, and Rhoades introduced such a notion for SYT, but only of rectangular shapes. In this paper, we describe cyclic descents for SYT of various other shapes. Motivated by these findings, we define cyclic extensions of descent sets in a general context, and we show that they exist for SYT of almost all shapes. Finally we introduce the ring of cyclic quasisymmetric functions and apply it to analyze the distributions of cyclic descents over permutations and SYT.

Original languageEnglish
Pages (from-to)32-42
Number of pages11
JournalCEUR Workshop Proceedings
Volume2113
StatePublished - 2018
Event11th International Conference on Random and Exhaustive Generation of Combinatorial Structures, GASCom 2018 - Athens, Greece
Duration: 18 Jun 201820 Jun 2018

All Science Journal Classification (ASJC) codes

  • General Computer Science

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