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arXiv · 2406.01166

Quasisymmetric expansion of Hall-Littlewood symmetric functions

Darij Grinberg·Ekaterina A. Vassilieva
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Abstract

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 $t=-q$.

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Darij Grinberg, Ekaterina A. Vassilieva. 2024-06-03. Quasisymmetric expansion of Hall-Littlewood symmetric functions. https://arxiv.org/abs/2406.01166

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