%0 Journal Article
%T A Noncommutative Chromatic Symmetric Function
%A David D. Gebhard
%A Bruce E. Sagan
%J Mathematics
%D 1999
%I arXiv
%X Stanley associated with a graph G a symmetric function X_G which reduces to G's chromatic polynomial under a certain specialization of variables. He then proved various theorems generalizing results about the chromatic polynomial, as well as new ones that cannot be interpreted at that level. Unfortunately, X_G does not satisfy a Deletion-Contraction Law which makes it difficult to apply induction. We introduce a symmetric function in noncommuting variables which does have such a law and specializes to X_G when the variables are allowed to commute. This permits us to further generalize some of Stanley's theorems and prove them in a uniform and straightforward manner. Furthermore, we make some progress on the (3+1)-free Conjecture of Stanley and Stembridge.
%U http://arxiv.org/abs/math/9907076v1