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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.20967 |
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| _version_ | 1866912729850183680 |
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| author | Van Nimwegen, Nicholas |
| author_facet | Van Nimwegen, Nicholas |
| contents | In a previous work, Bóna and Pantone studied permutations that avoided all but one pattern of length $k$ that began with a length $k-1$ increasing subsequence. We draw the connection between that idea and distant patterns, first discussed heavily in a work by Dimitrov, and study similar permutation classes, where the index not part of the increasing subsequence can vary. We find a large class of Wilf-Equivalences between $k+1$ classes of $k$ patterns of length $k+1$, and outline several classes of unbalanced Wilf-Equivalences related to the first class. Using this, we are also find new bounds on the exponential growth rate on all monotone distant patterns with a single gap constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permutations Almost Avoiding Monotone Distant Patterns Van Nimwegen, Nicholas Combinatorics In a previous work, Bóna and Pantone studied permutations that avoided all but one pattern of length $k$ that began with a length $k-1$ increasing subsequence. We draw the connection between that idea and distant patterns, first discussed heavily in a work by Dimitrov, and study similar permutation classes, where the index not part of the increasing subsequence can vary. We find a large class of Wilf-Equivalences between $k+1$ classes of $k$ patterns of length $k+1$, and outline several classes of unbalanced Wilf-Equivalences related to the first class. Using this, we are also find new bounds on the exponential growth rate on all monotone distant patterns with a single gap constraint. |
| title | Permutations Almost Avoiding Monotone Distant Patterns |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.20967 |