Séminaire Lotharingien de Combinatoire, 91B.86 (2024), 12 pp.
Darij Grinberg and Ekaterina A. Vassilieva
Quasisymmetric Expansion of Hall-Littlewood Symmetric Functions
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.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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