Plethysms of Chromatic and Tutte Symmetric Functions
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Date
2022
Authors
Spirkl, Sophie
Crew, Logan
Journal Title
Journal ISSN
Volume Title
Publisher
The Electronic Journal of Combinatorics
Abstract
Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients of Schur function plethysms is a major open question.
In this paper, we introduce a graph-theoretic interpretation for any plethysm based on the chromatic symmetric function. We use this interpretation to give simple proofs of new and previously known plethystic identities, as well as chromatic symmetric function identities.
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Keywords
tutte symmetric functions, plethysms