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arXiv · 2512.21086

Extending Results on Wilf-Equivalence of Partial Shuffles

Michael Albert·Dominic Searles·Matthew Slattery-Holmes
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Abstract

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.

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Michael Albert, Dominic Searles, Matthew Slattery-Holmes. 2025-12-24. Extending Results on Wilf-Equivalence of Partial Shuffles. https://arxiv.org/abs/2512.21086

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