Enumerating Permutations Avoiding Split Patterns 3|12 and 23|1
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914693114757120 |
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| author | Grigsby, Travis Richmond, Edward |
| author_facet | Grigsby, Travis Richmond, Edward |
| contents | In this paper, we give a formula for the number of permutations that avoid the split patterns $3|12$ and $23|1$ with respect to a position $r$. Such permutations count the number of Schubert varieties for which the projection map from the flag variety to a Grassmannian induces a fiber bundle structure. We also study the corresponding bivariate generating function and show how it is related to modified Bessel functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17654 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumerating Permutations Avoiding Split Patterns 3|12 and 23|1 Grigsby, Travis Richmond, Edward Combinatorics Algebraic Geometry 05A05 (Primary) 14N10 (Secondary) In this paper, we give a formula for the number of permutations that avoid the split patterns $3|12$ and $23|1$ with respect to a position $r$. Such permutations count the number of Schubert varieties for which the projection map from the flag variety to a Grassmannian induces a fiber bundle structure. We also study the corresponding bivariate generating function and show how it is related to modified Bessel functions. |
| title | Enumerating Permutations Avoiding Split Patterns 3|12 and 23|1 |
| topic | Combinatorics Algebraic Geometry 05A05 (Primary) 14N10 (Secondary) |
| url | https://arxiv.org/abs/2402.17654 |