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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.05939 |
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| _version_ | 1866909485511999488 |
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| author | Alexandersson, Per Jal, Aryaman Quemener, Maena |
| author_facet | Alexandersson, Per Jal, Aryaman Quemener, Maena |
| contents | We introduce rook-Eulerian polynomials, a generalization of the classical Eulerian polynomials arising from complete rook placements on Ferrers boards, and prove that they are real-rooted. We show that a natural context in which to interpret these rook placements is as lower intervals of $312$-avoiding permutations in the Bruhat order. We end with some variations and generalizations along this theme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real-rootedness of rook-Eulerian polynomials Alexandersson, Per Jal, Aryaman Quemener, Maena Combinatorics 5A15, 05A15, 26C10 We introduce rook-Eulerian polynomials, a generalization of the classical Eulerian polynomials arising from complete rook placements on Ferrers boards, and prove that they are real-rooted. We show that a natural context in which to interpret these rook placements is as lower intervals of $312$-avoiding permutations in the Bruhat order. We end with some variations and generalizations along this theme. |
| title | Real-rootedness of rook-Eulerian polynomials |
| topic | Combinatorics 5A15, 05A15, 26C10 |
| url | https://arxiv.org/abs/2502.05939 |