A categorification of the chromatic symmetric function

作者：Sazdanovic Radmila^*; Yip Martha

来源：Journal of Combinatorial Theory - Series A, 2018, 154: 218-246.

DOI：10.1016/j.jcta.2017.08.014

• Symmetric functions
• Chromatic polynomial
• Khovanov homology
• Representations
• Frobenius series
• Graph coloring

The Stanley chromatic symmetric function X-G of a graph G is a symmetric function generalization of the chromatic polynomial and has interesting combinatorial properties. We apply the ideas from Khovanov homology to construct a homology theory of graded G(n)-modules, whose graded Frobenius series Frob(G)(q, t) specializes to the chromatic symmetric function at q = t = 1. This homology theory can be thought of as a categorification of the chromatic symmetric function, and it satisfies homological analogues of several familiar properties of XG. In particular, the decomposition formula for XG discovered recently by Orellana, Scott, and independently by Guay-Paquet, is lifted to a long exact sequence in homology.

• 出版日期2018-2