The algebra of extended peaks
| Autor: | Grinberg, Darij, Vassilieva, Ekaterina A. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | S\'eminaire Lotharingien de Combinatoire 89B (2023), Proceedings of the 35th Conference on Formal Power Series 2023, Article #46 |
| Druh dokumentu: | Working Paper |
| Popis: | Building up on our previous works regarding $q$-deformed $P$-partitions, we introduce a new family of subalgebras for the ring of quasisymmetric functions. Each of these subalgebras admits as a basis a $q$-analogue to Gessel's fundamental quasisymmetric functions where $q$ is equal to a complex root of unity. Interestingly, the basis elements are indexed by sets corresponding to an intermediary statistic between peak and descent sets of permutations that we call extended peak. Comment: 12 pages; extended abstract submitted for FPSAC. Longform papers on the project are still forthcoming |
| Databáze: | arXiv |
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