Proper caterpillars are distinguished by their symmetric chromatic function
Combinatorics
2012-08-14 v1
Abstract
This paper deals with the so-called Stanley conjecture, which asks whether they are non-isomorphic trees with the same symmetric function generalization of the chromatic polynomial. By establishing a correspondence between caterpillars trees and integer compositions, we prove that caterpillars in a large class (we call trees in this class proper) have the same symmetric chromatic function generalization of the chromatic polynomial if and only if they are isomorphic.
Cite
@article{arxiv.1208.2267,
title = {Proper caterpillars are distinguished by their symmetric chromatic function},
author = {José Aliste-Prieto and José Zamora},
journal= {arXiv preprint arXiv:1208.2267},
year = {2012}
}