Abstract
The Stanley chromatic symmetric polynomial of a graph G is a symmetric function generalization of the chromatic polynomial, and has interesting combinatorial properties. We apply the techniques of Khovanov homology to construct a homology H∗(G) of graded Sn-modules, whose bigraded Frobenius series FrobG(q, t) reduces to the chromatic symmetric polynomial at q = t = 1. We also obtain analogues of several familiar properties of the chromatic symmetric polynomials in terms of homology.
| Original language | English |
|---|---|
| Pages (from-to) | 631-642 |
| Number of pages | 12 |
| Journal | Discrete Mathematics and Theoretical Computer Science |
| State | Published - 2015 |
| Event | 27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of Duration: Jul 6 2015 → Jul 10 2015 |
Bibliographical note
Funding Information:The former author would like to thank the Simons Foundation for its support via the AMS Travel and Simons Collaboration grants. The latter author would like to thank Chris Hays for helpful suggestions.
Publisher Copyright:
© 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France
Keywords
- Chromatic polynomial
- Frobenius series
- Graph colouring
- Khovanov homology
- Sn-modules
- Symmetric functions
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)
- Discrete Mathematics and Combinatorics