We express the integral form Macdonald polynomials as a weighted sum of Shareshian and Wachs' chromatic quasisymmetric functions of certain graphs. Then we use known expansions of these chromatic quasisymmetric functions into Schur and power sum symmetric functions to provide Schur and power sum formulas for the integral form Macdonald polynomials. Since the (integral form) Jack polynomials are a specialization of integral form Macdonald polynomials, we obtain analogous formulas for Jack polynomials as corollaries.
@article{10_37236_9011,
author = {James Haglund and Andrew Timothy Wilson},
title = {Macdonald polynomials and chromatic quasisymmetric functions},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {3},
doi = {10.37236/9011},
zbl = {1446.05090},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9011/}
}
TY - JOUR
AU - James Haglund
AU - Andrew Timothy Wilson
TI - Macdonald polynomials and chromatic quasisymmetric functions
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/9011/
DO - 10.37236/9011
ID - 10_37236_9011
ER -
%0 Journal Article
%A James Haglund
%A Andrew Timothy Wilson
%T Macdonald polynomials and chromatic quasisymmetric functions
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/9011/
%R 10.37236/9011
%F 10_37236_9011
James Haglund; Andrew Timothy Wilson. Macdonald polynomials and chromatic quasisymmetric functions. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9011
