Results 141 to 148 of about 2,074 (148)

α-Chromatic Symmetric Functions

International Mathematics Research Notices
Abstract In this paper, we introduce the $\alpha $-chromatic symmetric functions  $\chi ^{(\alpha )}_\pi [X;q]$, extending Shareshian and Wachs’ chromatic symmetric functions with an additional real parameter $\alpha $. We present positive combinatorial formulas with explicit interpretations.
Haglund, Jim, Oh, Jaeseong, Yoo, Meesue
openaire   +1 more source

Chromatic symmetric function of graphs from Borcherds algebras

Journal of Combinatorial Theory - Series A, 2021
G Arunkumar
exaly  

Caterpillars, ribbons, and the chromatic symmetric function

2009
For every n-vertex tree T, it is known that the chromatic polynomial x(T, k) is equal to k(k — l )ⁿ⁻¹. It is known that the function in noncommuting variables, Y[sub G](x), distinguishes all simple graphs. In the midground, the question of whether or not the chromatic symmetric function X[sub G](x) distinguishes nonisomorphic trees is still open.
openaire   +1 more source

A categorification of the chromatic symmetric function

Journal of Combinatorial Theory - Series A, 2018
Radmila Sazdanovic
exaly  

A combinatorial formula for the Schur coefficients of chromatic symmetric functions

Discrete Applied Mathematics, 2020
David G L Wang
exaly  

On $e$-Positivity and $e$-Unimodality of Chromatic Quasi-symmetric Functions

SIAM Journal on Discrete Mathematics, 2019
Soojin Cho
exaly  

The e-positivity of the chromatic symmetric function for twinned paths and cycles

Discrete Mathematics
Sheila Sundaram
exaly  

A graph polynomial from chromatic symmetric functions

Journal of Graph Theory
Logan Crew
exaly