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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.07581 |
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| _version_ | 1866915415262756864 |
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| author | Chen, L. He, Y. T. Wang, David G. L. |
| author_facet | Chen, L. He, Y. T. Wang, David G. L. |
| contents | Along with his confirmation of the $e$-positivity of all cycle-chord graphs $θ_{ab1}$, the third author conjectured the $e$-positivity of all theta graphs $θ_{abc}$. In this paper, we establish the $e$-positivity of all clock graphs $θ_{ab2}$ by using the composition method. The key idea is to investigate the fibers of certain partial reversal transformation on compositions with all parts at least $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Clocks are $e$-positive Chen, L. He, Y. T. Wang, David G. L. Combinatorics 05E05 Along with his confirmation of the $e$-positivity of all cycle-chord graphs $θ_{ab1}$, the third author conjectured the $e$-positivity of all theta graphs $θ_{abc}$. In this paper, we establish the $e$-positivity of all clock graphs $θ_{ab2}$ by using the composition method. The key idea is to investigate the fibers of certain partial reversal transformation on compositions with all parts at least $2$. |
| title | Clocks are $e$-positive |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2410.07581 |