The Enumeration of Permutations Avoiding 3124 and 4312

TL;DR

This paper derives the generating function for permutations avoiding patterns 3124 and 4312 by representing them as inflations of specific geometric grid classes, advancing understanding of pattern-avoiding permutations.

Contribution

It introduces a novel approach by expressing these permutations as inflations of geometric grid classes, providing a new method to analyze pattern avoidance.

Findings

Generated explicit formulas for the avoidance class

Connected permutation avoidance to geometric grid structures

Enhanced enumeration techniques for pattern-avoiding permutations

Abstract

We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classes.