A signed $e$-expansion of the chromatic quasisymmetric function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916238406451200 |
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| author | Tom, Foster |
| author_facet | Tom, Foster |
| contents | We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution to prove a new combinatorial formula for K-chains, which are graphs formed by joining cliques at single vertices. This formula immediately implies $e$-positivity and $e$-unimodality for K-chains. We also prove a version of our signed $e$-expansion for arbitrary graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08020 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A signed $e$-expansion of the chromatic quasisymmetric function Tom, Foster Combinatorics 05E05 (Primary) 05E10, 05C15 (Secondary) We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution to prove a new combinatorial formula for K-chains, which are graphs formed by joining cliques at single vertices. This formula immediately implies $e$-positivity and $e$-unimodality for K-chains. We also prove a version of our signed $e$-expansion for arbitrary graphs. |
| title | A signed $e$-expansion of the chromatic quasisymmetric function |
| topic | Combinatorics 05E05 (Primary) 05E10, 05C15 (Secondary) |
| url | https://arxiv.org/abs/2311.08020 |