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The algebra of extended peaks | | Darij Grinberg
; Ekaterina A. Vassilieva
; | | Date: |
1 Jan 2023 | | Abstract: | 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. | | Source: | arXiv, 2301.00309 | | Services: | Forum | Review | PDF | Favorites | |
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