On cyclic descents for tableaux.

Ron Adin, Yuval Roichman, Victor Reiner

Research output: Contribution to journalConference articlepeer-review


The notion of descent set, for permutations as well as for standard Young tableaux (SYT), is classical. Cellini introduced a natural notion of cyclic descent set for permutations, and Rhoades introduced such a notion for SYT - but only for rectangular shapes. In this work we define cyclic extensions of descent sets in a general context, and prove existence and essential uniqueness for SYT of almost all shapes. The proof applies nonnegativity properties of Postnikov's toric Schur polynomials, providing a new interpretation of certain Gromov-Witten invariants.
Original languageAmerican English
Number of pages12
JournalSeminaire Lotharingien de Combinatoire
StatePublished - 2018


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