Forest webs and pattern avoidance
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908896794247168 |
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| author | Striker, Jessica Tenner, Bridget Eileen |
| author_facet | Striker, Jessica Tenner, Bridget Eileen |
| contents | In a recent preprint, Mike Cummings showed that the smooth components of suitably parametrized Springer fibers are in bijection with contracted, fully reduced Plücker degree-two $\mathfrak{sl}_r$-webs of standard type and that are forests. He showed these are enumerated by sequence A116731 in the OEIS, which is equinumerous with permutations avoiding the patterns {321,2143,3124}. Cummings posed the problem of strengthening this enumerative result by finding a bijection between these webs and a collection of pattern-avoiding permutations. Here we solve this problem, although notably not with the collection of patterns that Cummings had proposed. Rather, we give a bijection between this class of webs and permutations avoiding the patterns {132,4321,3214}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17287 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forest webs and pattern avoidance Striker, Jessica Tenner, Bridget Eileen Combinatorics Primary: 05A05, Secondary: 05E10, 05A15 In a recent preprint, Mike Cummings showed that the smooth components of suitably parametrized Springer fibers are in bijection with contracted, fully reduced Plücker degree-two $\mathfrak{sl}_r$-webs of standard type and that are forests. He showed these are enumerated by sequence A116731 in the OEIS, which is equinumerous with permutations avoiding the patterns {321,2143,3124}. Cummings posed the problem of strengthening this enumerative result by finding a bijection between these webs and a collection of pattern-avoiding permutations. Here we solve this problem, although notably not with the collection of patterns that Cummings had proposed. Rather, we give a bijection between this class of webs and permutations avoiding the patterns {132,4321,3214}. |
| title | Forest webs and pattern avoidance |
| topic | Combinatorics Primary: 05A05, Secondary: 05E10, 05A15 |
| url | https://arxiv.org/abs/2603.17287 |