A combinatorial formula for the Schur coefficients of chromatic symmetric functions
| Autor: | David G. L. Wang, Monica M. Y. Wang |
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| Rok vydání: | 2020 |
| Předmět: |
Combinatorial formula
Mathematics::Combinatorics Applied Mathematics 0211 other engineering and technologies 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology 01 natural sciences Graph Combinatorics Symmetric function Partition method 010201 computation theory & mathematics Discrete Mathematics and Combinatorics Chromatic scale Mathematics::Representation Theory Mathematics |
| Zdroj: | Discrete Applied Mathematics. 285:621-630 |
| ISSN: | 0166-218X |
| Popis: | We provide a formula for every Schur coefficient in the chromatic symmetric function of a graph in terms of special rim hook tabloids. This formula is useful in confirming the non-Schur positivity of the chromatic symmetric function of a graph, especially when Stanley’s stable partition method does not work. As applications, we completely characterize Schur positive complete tripartite graphs. We show that any squid graph obtained by attaching n pendent edges to a common vertex on the cycle C m is not Schur positive if m ≠ 2 n − 1 , and that any pineapple graph obtained by attaching m pendent edges to a common vertex on the complete graph K n is not Schur positive if n ≤ 2 m − 2 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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