Séminaire Lotharingien de Combinatoire, 89B.46 (2023), 12 pp.
Darij Grinberg and Ekaterina A. Vassilieva
The Algebra of Extended Peaks
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.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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