Pattern Avoiding Permutations as Walks
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908728043765760 |
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| author | Franklín, Atli Fannar |
| author_facet | Franklín, Atli Fannar |
| contents | The Stanley-Wilf limit of the pattern 1324 is known to lie between 10.271 and 13.5. We obtain lower bounds on this limit by encoding permutations as walks in directed graphs: building a permutation by successive insertion of maxima corresponds to traversing edges, and the growth rate of walks equals the spectral radius of the adjacency matrix. For 1324, this graph is too large for direct computation, so we pass to a quotient graph with weighted edges. Conditional on a natural conjecture, this yields a lower bound of 10.418. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19462 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pattern Avoiding Permutations as Walks Franklín, Atli Fannar Combinatorics 05A05 The Stanley-Wilf limit of the pattern 1324 is known to lie between 10.271 and 13.5. We obtain lower bounds on this limit by encoding permutations as walks in directed graphs: building a permutation by successive insertion of maxima corresponds to traversing edges, and the growth rate of walks equals the spectral radius of the adjacency matrix. For 1324, this graph is too large for direct computation, so we pass to a quotient graph with weighted edges. Conditional on a natural conjecture, this yields a lower bound of 10.418. |
| title | Pattern Avoiding Permutations as Walks |
| topic | Combinatorics 05A05 |
| url | https://arxiv.org/abs/2512.19462 |