# Enumerations of some pattern-avoiding Fishburn permutations

## TL;DR

This paper proves conjectures related to counting specific classes of pattern-avoiding Fishburn permutations, including those avoiding pattern 321 and certain classical patterns of sizes 4 and 5.

## Contribution

It confirms two conjectures by Egge and provides enumeration results for Fishburn permutations avoiding particular classical patterns.

## Key findings

- Enumeration of Fishburn permutations avoiding pattern 321 and certain classical patterns.
- Proof of two conjectures of Egge regarding pattern-avoiding Fishburn permutations.
- Enumeration formulas for these classes of permutations.

## Abstract

In this paper, we prove two conjectures of Egge on the enumeration of several classes of pattern-avoiding Fishburn permutations. Our results include enumerating Fishburn permutations avoiding pattern 321 and one of the following three types of classical patterns: a pattern of size 4, two patterns of size 4, or a pattern of size 5.