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 language||English (US)|
|State||Published - 2018|
|Event||30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States|
Duration: Jul 16 2018 → Jul 20 2018
|Conference||30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018|
|Period||7/16/18 → 7/20/18|
Bibliographical noteFunding Information:
∗firstname.lastname@example.org. Partially supported by by a MISTI MIT-Israel grant. †email@example.com. Partially supported by NSF grant DMS-1601961. ‡firstname.lastname@example.org. Partially supported by by a MISTI MIT-Israel grant.
- Cyclic descent
- Gromov-Witten invariant
- Ribbon Schur function
- Standard Young tableau