Quasisymmetric expansion of Hall-Littlewood symmetric functions

Fuente: arXiv
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Main Authors: Grinberg, Darij, Vassilieva, Ekaterina A.
Format: Preprint
Published: 2024
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_version_ 1866914996520222720
author Grinberg, Darij
Vassilieva, Ekaterina A.
author_facet Grinberg, Darij
Vassilieva, Ekaterina A.
contents In our previous works we introduced a $q$-deformation of the generating functions for enriched $P$-partitions. We call the evaluation of this generating functions on labelled chains, the $q$-fundamental quasisymmetric functions. These functions interpolate between Gessel's fundamental ($q=0$) and Stembridge's peak ($q=1$) functions, the natural quasisymmetric expansions of Schur and Schur's $Q$-symmetric functions. In this paper, we show that our $q$-fundamental functions provide a quasisymmetric expansion of Hall-Littlewood $S$-symmetric functions with parameter $t=-q$.
format Preprint
id arxiv_https___arxiv_org_abs_2406_01166
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quasisymmetric expansion of Hall-Littlewood symmetric functions
Grinberg, Darij
Vassilieva, Ekaterina A.
Combinatorics
05E05, 06A11
In our previous works we introduced a $q$-deformation of the generating functions for enriched $P$-partitions. We call the evaluation of this generating functions on labelled chains, the $q$-fundamental quasisymmetric functions. These functions interpolate between Gessel's fundamental ($q=0$) and Stembridge's peak ($q=1$) functions, the natural quasisymmetric expansions of Schur and Schur's $Q$-symmetric functions. In this paper, we show that our $q$-fundamental functions provide a quasisymmetric expansion of Hall-Littlewood $S$-symmetric functions with parameter $t=-q$.
title Quasisymmetric expansion of Hall-Littlewood symmetric functions
topic Combinatorics
05E05, 06A11
url https://arxiv.org/abs/2406.01166