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Positive expansions of extended Schur functions in the Young quasisymmetric Schur basis

Chloe’ Marcum and Elizabeth Niese
Vol. 17 (2024), No. 2, 217–232
DOI: 10.2140/involve.2024.17.217
Abstract

There are a number of Schur-like bases for the quasisymmetric functions. Extended Schur functions, introduced by Assaf and Searles, expand positively in the Young quasisymmetric Schur basis for certain indexing compositions. We establish this expansion using an algorithm defined by Allen, Hallam, and Mason restricted to the generating objects of the extended Schur functions.

Keywords
quasisymmetric functions, Schur polynomials, extended Schur functions, dual immaculate functions
Mathematical Subject Classification
Primary: 05E05
Milestones
Received: 18 June 2021
Revised: 25 January 2023
Accepted: 23 February 2023
Published: 20 May 2024

Communicated by Kenneth S. Berenhaut
Authors
Chloe’ Marcum
University of Kentucky
Lexington, KY
United States
Elizabeth Niese
Marshall University
Huntington, WV
United States
© 2024 MSP (Mathematical Sciences Publishers).