A composition method for neat formulas of chromatic symmetric functions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916491352342528 |
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| author | Wang, David G. L. Zhou, James Z. F. |
| author_facet | Wang, David G. L. Zhou, James Z. F. |
| contents | We develop a composition method to unearth positive $e_I$-expansions of chromatic symmetric functions $X_G$, where the subscript $I$ stands for compositions rather than integer partitions. Using this method, we derive positive and neat $e_I$-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the $e$-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A composition method for neat formulas of chromatic symmetric functions Wang, David G. L. Zhou, James Z. F. Combinatorics 05E05, 05A15 We develop a composition method to unearth positive $e_I$-expansions of chromatic symmetric functions $X_G$, where the subscript $I$ stands for compositions rather than integer partitions. Using this method, we derive positive and neat $e_I$-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the $e$-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles. |
| title | A composition method for neat formulas of chromatic symmetric functions |
| topic | Combinatorics 05E05, 05A15 |
| url | https://arxiv.org/abs/2401.01027 |