Geodesic
The Kernel of Chromatic Quasisymmetric Functions on Graphs and Nestohedra
Séminaire lotharingien de combinatoire, 80B (2018) 
Raul Penaguiao. The Kernel of Chromatic Quasisymmetric Functions on Graphs and Nestohedra. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a9/
@article{SLC_2018_80B_a9,
     author = {Raul Penaguiao},
     title = {The {Kernel} of {Chromatic} {Quasisymmetric} {Functions} on {Graphs} and {Nestohedra}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a9/}
}
TY  - JOUR
AU  - Raul Penaguiao
TI  - The Kernel of Chromatic Quasisymmetric Functions on Graphs and Nestohedra
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a9/
ID  - SLC_2018_80B_a9
ER  - 
%0 Journal Article
%A Raul Penaguiao
%T The Kernel of Chromatic Quasisymmetric Functions on Graphs and Nestohedra
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a9/
%F SLC_2018_80B_a9

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We study the chromatic symmetric function on graphs, and show that its kernel is spanned by the modular relations. We generalise this result to the chromatic quasisymmetric function on nestohedra, a family of generalised permutahedra. We use this description of the kernel of the chromatic symmetric function to find other graph invariants that may help us tackle the tree conjecture.