Counting Signed Vexillary Permutations

TL;DR

This paper proves that the number of signed permutations avoiding the pattern 1234 is equal to those avoiding 2143, confirming a conjecture and using generating trees as the main method.

Contribution

It establishes the equality in enumeration of two classes of signed permutations avoiding specific patterns, resolving a conjecture by Anderson and Fulton.

Findings

Number of signed permutations avoiding 1234 equals those avoiding 2143

Use of generating trees to analyze pattern avoidance

Provides new directions for further research

Abstract

We show that the number of signed permutations avoiding 1234 equals the number of signed permutations avoiding 2143 (also called vexillary signed permutations), resolving a conjecture by Anderson and Fulton. The main tool that we use is the generating tree developed by West. Many further directions are mentioned in the end.