The ring of cyclic quasi-symmetric functions is introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; they arise as toric P-partition enumerators, for toric posets P with a total cyclic order. The associated structure constants are determined by cyclic shuffles of permutations. For every non-hook shape l, the coefficients in the expansion of the Schur function sl in terms of fundamental cyclic quasi-symmetric functions are nonnegative. The theory has applications to the enumeration of cyclic shuffles and SYT by cyclic descents.
|Original language||English (US)|
|State||Published - 2019|
|Event||31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia|
Duration: Jul 1 2019 → Jul 5 2019
|Conference||31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019|
|Period||7/1/19 → 7/5/19|