Pattern avoiding permutations and independent sets in graphs

TL;DR

This paper presents a novel encoding method that links pattern-avoiding permutations to independent sets in specific graphs, enabling enumeration based on boundary points and independent set size.

Contribution

It introduces a new graph-based encoding technique for pattern-avoiding permutations, facilitating their enumeration and analysis.

Findings

Enumerates specific pattern-avoiding permutations using the new encoding.

Establishes a correspondence between permutation patterns and independent sets in graphs.

Provides formulas or methods for counting permutations based on boundary points and independent set size.

Abstract

We introduce a new method for encoding permutations as weighted independent sets in a family of graphs we call cores. The encoding allows us to enumerate (1324, 2143)-, (1234, 1324, 2143)-, (1234, 1324, 1432, 3214)-avoiding permutations with respect to their number of "boundary points" and the size of the independent set in the graph they correspond to.