Cyclic quasi-symmetric functions
| Autor: | Adin, Ron M., Gessel, Ira M., Reiner, Victor, Roichman, Yuval |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The ring of cyclic quasi-symmetric functions and its non-Escher subring are introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; for the non-Escher subring 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. We then prove the following positivity phenomenon: for every non-hook shape $\lambda$, the coefficients in the expansion of the Schur function $s_\lambda$ in terms of fundamental cyclic quasi-symmetric functions are nonnegative. The proof relies on the existence of a cyclic descent map on the standard Young tableaux (SYT) of shape $\lambda$. The theory has applications to the enumeration of cyclic shuffles and SYT by cyclic descents. Comment: 38 pages, added references and updated last section |
| Databáze: | arXiv |
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