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.
Bibliographical noteFunding Information:
This work was partially supported by a MIT-Israel International Science and Technology Initiatives grant [to R.M.A. and Y.R.] and a National Science Foundation grant [DMS-1601961 to V.R.].
© 2018 The Author(s).