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 language||English (US)|
|Number of pages||11|
|Journal||CEUR Workshop Proceedings|
|State||Published - 2018|
|Event||11th International Conference on Random and Exhaustive Generation of Combinatorial Structures, GASCom 2018 - Athens, Greece|
Duration: Jun 18 2018 → Jun 20 2018