A categorification of the chromatic symmetric function
| Autor: | Radmila Sazdanovic, Martha Yip |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Khovanov homology
Categorification 0102 computer and information sciences Homology (mathematics) Chromatic polynomial 01 natural sciences Theoretical Computer Science Combinatorics Mathematics - Geometric Topology Mathematics - Quantum Algebra FOS: Mathematics Mathematics - Combinatorics Quantum Algebra (math.QA) Discrete Mathematics and Combinatorics Chromatic scale Graph coloring 0101 mathematics Mathematics::Symplectic Geometry Mathematics Exact sequence Mathematics::Combinatorics 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology Symmetric function Computational Theory and Mathematics 010201 computation theory & mathematics Combinatorics (math.CO) |
| Zdroj: | Journal of Combinatorial Theory, Series A. 154:218-246 |
| ISSN: | 0097-3165 |
| DOI: | 10.1016/j.jcta.2017.08.014 |
| Popis: | 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 of Khovanov homology to construct a homology of graded $S_n$-modules, whose graded Frobenius series $Frob_G(q,t)$ reduces to the chromatic symmetric function at $q=t=1$. This homology can be thought of as a categorification of the chromatic symmetric function, and provides a homological analogue of several familiar properties of $X_G$. In particular, the decomposition formula for $X_G$ discovered recently by Orellana and Scott, and Guay-Paquet is lifted to a long exact sequence in homology. Comment: 26 pages |
| Databáze: | OpenAIRE |
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