Extending Results on Wilf-Equivalence of Partial Shuffles
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914218801889280 |
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| author | Albert, Michael Searles, Dominic Slattery-Holmes, Matthew |
| author_facet | Albert, Michael Searles, Dominic Slattery-Holmes, Matthew |
| contents | In 2020, Bloom and Sagan defined subsets of the symmetric group $\mathfrak{S}_n$ called partial shuffles, and proved a formula for the Schur expansion of the pattern quasisymmetric function associated with a partial shuffle. In their proof, they establish that any two partial shuffles of the same size are Wilf-equivalent. We give an alternative proof of this fact, using an iterative approach. We also show that Wilf-equivalence is preserved on including a decreasing pattern in partial shuffles, and we provide some enumerative results for avoidance classes whose bases consist of a partial shuffle and a decreasing permutation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Results on Wilf-Equivalence of Partial Shuffles Albert, Michael Searles, Dominic Slattery-Holmes, Matthew Combinatorics 05A05, 05A15 In 2020, Bloom and Sagan defined subsets of the symmetric group $\mathfrak{S}_n$ called partial shuffles, and proved a formula for the Schur expansion of the pattern quasisymmetric function associated with a partial shuffle. In their proof, they establish that any two partial shuffles of the same size are Wilf-equivalent. We give an alternative proof of this fact, using an iterative approach. We also show that Wilf-equivalence is preserved on including a decreasing pattern in partial shuffles, and we provide some enumerative results for avoidance classes whose bases consist of a partial shuffle and a decreasing permutation. |
| title | Extending Results on Wilf-Equivalence of Partial Shuffles |
| topic | Combinatorics 05A05, 05A15 |
| url | https://arxiv.org/abs/2512.21086 |