Abstract
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) |
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| 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
| Conference | 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 |
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| Country/Territory | United States |
| City | Hanover |
| Period | 7/16/18 → 7/20/18 |
Bibliographical note
Funding Information:∗radin@math.biu.ac.il. Partially supported by by a MISTI MIT-Israel grant. †reiner@math.umn.edu. Partially supported by NSF grant DMS-1601961. ‡yuvalr@math.biu.ac.il. Partially supported by by a MISTI MIT-Israel grant.
Publisher Copyright:
© FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.
Keywords
- Cyclic descent
- Descent
- Gromov-Witten invariant
- Ribbon Schur function
- Standard Young tableau