In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if $\{ G_ k \} _{k\geq 1}$ is a set of connected graphs such that $G_k$ has $k$ vertices for each $k$, then the set of all chromatic symmetric functions $\{ X_{G_ k} \} _{k\geq 1}$ generates the algebra of symmetric functions. We also obtain explicit expressions for the generators arising from complete graphs, star graphs, path graphs and cycle graphs.
@article{10_37236_5540,
author = {Soojin Cho and Stephanie van Willigenburg},
title = {Chromatic bases for symmetric functions},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {1},
doi = {10.37236/5540},
zbl = {1329.05295},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5540/}
}
TY - JOUR
AU - Soojin Cho
AU - Stephanie van Willigenburg
TI - Chromatic bases for symmetric functions
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/5540/
DO - 10.37236/5540
ID - 10_37236_5540
ER -
%0 Journal Article
%A Soojin Cho
%A Stephanie van Willigenburg
%T Chromatic bases for symmetric functions
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/5540/
%R 10.37236/5540
%F 10_37236_5540
Soojin Cho; Stephanie van Willigenburg. Chromatic bases for symmetric functions. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/5540
