On permutations avoiding the dashed patterns 32-41 and 41-32

TL;DR

This paper establishes a combinatorial equivalence between permutations avoiding specific dashed patterns and indecomposable set partitions, revealing new connections in permutation pattern avoidance.

Contribution

It introduces a novel bijection linking pattern-avoiding permutations to indecomposable set partitions, expanding understanding of permutation pattern classes.

Findings

Permutations avoiding 32-41 and 41-32 are equinumerous with indecomposable set partitions.

A related combinatorial result is deduced from this equivalence.

Abstract

We show that permutations of size $n$ avoiding both of the dashed patterns 32-41 and 41-32 are equinumerous with indecomposable set partitions of size $n+1$, and deduce a related result.