A new record for $1324$-avoiding permutations

TL;DR

This paper improves the upper bound on the number of permutations avoiding the pattern 1324 by refining previous counting methods, advancing understanding of permutation pattern avoidance.

Contribution

It introduces a refined counting argument that yields a tighter upper bound for 1324-avoiding permutations, improving upon prior bounds.

Findings

Established a new upper bound for 1324-avoiding permutations

Refined existing counting techniques for permutation patterns

Enhanced understanding of permutation avoidance complexity

Abstract

Refining an existing counting argument, we provide an improved upper bound for the number of 1324-avoiding permutations of a given length.