The spiders $S(4m+2,\,2m,\,1)$ are $e$-positive
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909760373129216 |
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| author | Tang, Davion Q. B. Wang, David G. L. Wang, Monica M. Y. |
| author_facet | Tang, Davion Q. B. Wang, David G. L. Wang, Monica M. Y. |
| contents | By using the composition method, we establish the $e$-positivity of spiders of the form $S(4m+2,\, 2m,\, 1)$, which was conjectured by Aliniaeifard, van Willigenburg and Wang. Following the divide-and-conquer strategy, we group one or two $e_J$-terms that have positive coefficients with each $e_I$-term that has a negative coefficient, where the compositions $J$ are selected to be obtained by rearranging the parts of $I$, and show the positivity of the sum of those coefficients. Our main contribution is an explicit construction of the injection. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_04915 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The spiders $S(4m+2,\,2m,\,1)$ are $e$-positive Tang, Davion Q. B. Wang, David G. L. Wang, Monica M. Y. Combinatorics 05E05 05C15 05A20 By using the composition method, we establish the $e$-positivity of spiders of the form $S(4m+2,\, 2m,\, 1)$, which was conjectured by Aliniaeifard, van Willigenburg and Wang. Following the divide-and-conquer strategy, we group one or two $e_J$-terms that have positive coefficients with each $e_I$-term that has a negative coefficient, where the compositions $J$ are selected to be obtained by rearranging the parts of $I$, and show the positivity of the sum of those coefficients. Our main contribution is an explicit construction of the injection. |
| title | The spiders $S(4m+2,\,2m,\,1)$ are $e$-positive |
| topic | Combinatorics 05E05 05C15 05A20 |
| url | https://arxiv.org/abs/2405.04915 |