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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2301.00309
- arXiv:
- arXiv:2301.00309
- Bibcode:
- 2023arXiv230100309G
- Keywords:
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- Mathematics - Combinatorics;
- 05E05;
- 06A11
- E-Print:
- 12 pages