A new upper bound for 1324-avoiding permutations

TL;DR

This paper establishes a new upper bound on the number of permutations avoiding the pattern 1324, showing it grows at a rate less than (7+4√3)^n, refining previous estimates.

Contribution

It provides the first explicit exponential upper bound for 1324-avoiding permutations, improving understanding of their combinatorial growth rate.

Findings

Number of 1324-avoiding permutations < (7+4√3)^n

Refines previous bounds on permutation avoidance

Advances combinatorial enumeration techniques

Abstract

We prove that the number of 1324-avoiding permutations of length n is less than (7+4\sqrt{3})^n.