A short note on the Stanley-Wilf Conjecture for permutations on multisets

TL;DR

This paper extends the Stanley-Wilf Conjecture to permutations on multisets, providing a direct proof that the number of such permutations avoiding a pattern grows at most exponentially.

Contribution

It offers a direct proof that the Stanley-Wilf Conjecture applies to permutations on multisets, expanding its scope beyond permutations of distinct elements.

Findings

The Stanley-Wilf Conjecture holds for permutations on multisets.

Number of pattern-avoiding permutations on multisets grows at most exponentially.

The proof is direct and extends known results to a broader class of permutations.

Abstract

The concept of pattern avoidance respectively containment in permutations can be extended to permutations on multisets in a straightforward way. In this note we present a direct proof of the already known fact that the well-known Stanley-Wilf Conjecture, stating that the number of permutations avoiding a given pattern does not grow faster than exponentially, also holds for permutations on multisets.