Global patterns in signed permutations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915248792928256 |
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| author | Levens, Owen John Lewis, Joel Brewster Tenner, Bridget Eileen |
| author_facet | Levens, Owen John Lewis, Joel Brewster Tenner, Bridget Eileen |
| contents | Global permutation patterns have recently been shown to characterize important properties of a Coxeter group. Here we study global patterns in the context of signed permutations, with both characterizing and enumerative results. Surprisingly, many properties of signed permutations may be characterized by avoidance of the same set of patterns as the corresponding properties in the symmetric group. We also extend previous enumerative work of Egge, and our work has connections to the Garfinkle--Barbasch--Vogan correspondence, the Erdős--Szekeres theorem, and well-known integer sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global patterns in signed permutations Levens, Owen John Lewis, Joel Brewster Tenner, Bridget Eileen Combinatorics Primary: 05A05, Secondary: 20F55 and 05A15 Global permutation patterns have recently been shown to characterize important properties of a Coxeter group. Here we study global patterns in the context of signed permutations, with both characterizing and enumerative results. Surprisingly, many properties of signed permutations may be characterized by avoidance of the same set of patterns as the corresponding properties in the symmetric group. We also extend previous enumerative work of Egge, and our work has connections to the Garfinkle--Barbasch--Vogan correspondence, the Erdős--Szekeres theorem, and well-known integer sequences. |
| title | Global patterns in signed permutations |
| topic | Combinatorics Primary: 05A05, Secondary: 20F55 and 05A15 |
| url | https://arxiv.org/abs/2504.13108 |