Séminaire Lotharingien de Combinatoire, 86B.78 (2022), 12 pp.

Darij Grinberg and Ekaterina A. Vassilieva

A q-Deformation of Enriched P-Partitions

Abstract. We introduce a q-deformation that generalises in a single framework previous works on classical and enriched P-partitions. In particular, we build a new family of power series with a parameter q that interpolates between Gessel's fundamental (q=0) and Stembridge's peak quasisymmetric functions (q=1) and show that it is a basis of QSym when q∉{-1,1}. Furthermore we build their corresponding monomial bases parametrised with q that cover our previous work on enriched monomials and the essential quasisymmetric functions of Hoffman.


Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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