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.
@article{10_37236_10637,
author = {Logan Crew and Sophie Spirkl},
title = {Plethysms of chromatic and {Tutte} symmetric functions},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/10637},
zbl = {1497.05259},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10637/}
}
TY - JOUR
AU - Logan Crew
AU - Sophie Spirkl
TI - Plethysms of chromatic and Tutte symmetric functions
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10637/
DO - 10.37236/10637
ID - 10_37236_10637
ER -
%0 Journal Article
%A Logan Crew
%A Sophie Spirkl
%T Plethysms of chromatic and Tutte symmetric functions
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10637/
%R 10.37236/10637
%F 10_37236_10637
Logan Crew; Sophie Spirkl. Plethysms of chromatic and Tutte symmetric functions. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10637
