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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.01166 |
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| _version_ | 1866916556527632384 |
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| author | Wang, David G. L. |
| author_facet | Wang, David G. L. |
| contents | We establish the $e$-positivity of cycle-chord graphs by using the composition method which is developed by Zhou and the author recently. Our method is simpler than the $(e)$-positivity approach which is used for handling cycle-chords with girth at most $4$. We also provide a combinatorial interpretation of the $e$-coefficients, and conjecture that theta graphs are $e$-positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All cycle-chords are $e$-positive Wang, David G. L. Combinatorics 05E05 We establish the $e$-positivity of cycle-chord graphs by using the composition method which is developed by Zhou and the author recently. Our method is simpler than the $(e)$-positivity approach which is used for handling cycle-chords with girth at most $4$. We also provide a combinatorial interpretation of the $e$-coefficients, and conjecture that theta graphs are $e$-positive. |
| title | All cycle-chords are $e$-positive |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2405.01166 |