A $q$-deformation of enriched $P$-partitions (extended abstract) - Archive ouverte HAL
Article Dans Une Revue Seminaire Lotharingien de Combinatoire Année : 2022

A $q$-deformation of enriched $P$-partitions (extended abstract)

Résumé

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 $q\notin\{-1,1\}$. 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.

Dates et versions

hal-03870825 , version 1 (24-11-2022)

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Darij Grinberg, Ekaterina A. Vassilieva. A $q$-deformation of enriched $P$-partitions (extended abstract). Seminaire Lotharingien de Combinatoire, 2022. ⟨hal-03870825⟩
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