Adjacent cycle-chains are $e$-positive
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914996791803904 |
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| author | Tom, Foster Vailaya, Aarush |
| author_facet | Tom, Foster Vailaya, Aarush |
| contents | We describe a way to decompose the chromatic symmetric function as a positive sum of smaller pieces. We show that these pieces are $e$-positive for cycles. Then we prove that attaching a cycle to a graph preserves the $e$-positivity of these pieces. From this, we prove an $e$-positive formula for graphs of cycles connected at adjacent vertices. We extend these results to graphs formed by connecting a sequence of cycles and cliques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adjacent cycle-chains are $e$-positive Tom, Foster Vailaya, Aarush Combinatorics 05E05 (Primary) 05C15 (Secondary) We describe a way to decompose the chromatic symmetric function as a positive sum of smaller pieces. We show that these pieces are $e$-positive for cycles. Then we prove that attaching a cycle to a graph preserves the $e$-positivity of these pieces. From this, we prove an $e$-positive formula for graphs of cycles connected at adjacent vertices. We extend these results to graphs formed by connecting a sequence of cycles and cliques. |
| title | Adjacent cycle-chains are $e$-positive |
| topic | Combinatorics 05E05 (Primary) 05C15 (Secondary) |
| url | https://arxiv.org/abs/2410.21762 |