Cyclic descents for permutations and tableaux

The study of descents of permutations may be traced back to Euler, and is fundamental to contemporary algebraic combinatorics and its applications. A cyclic extension of this notion was introduced in the late 20th century.

The talk will focus on aspects of descents and cyclic descents for permutations and for standard Young tableaux. Following an axiomatization of the notion of a cyclic descent extension, we will characterize sets of combinatorial objects for which such an extension exists. The main results concern sets of standard Young tableaux of a fixed shape and sets of permutations of a fixed cycle type, i.e., conjugacy classes. The original proofs of both results were algebraic and not constructive, but in the case of tableaux a constructive proof was later given by Brice Huang.

Based on joint works with Pál Hegedüs, Vic Reiner and Yuval Roichman

No prior acquaintance is assumed.