Almost avoiding permutations

TL;DR

This paper explores the concept of 'almost avoiding' permutations, where a permutation nearly avoids a pattern by removing just one element, and studies the properties and implications of this notion.

Contribution

It introduces and formalizes the concept of almost avoiding permutations, providing new insights into permutation pattern avoidance with minimal modifications.

Findings

Characterization of almost avoiding permutations

Connections to classical pattern avoidance theory

Potential enumeration results for almost avoiding classes

Abstract

We investigate the notion of almost avoiding a permutation: $\pi$ almost avoids $\beta$ if one can remove a single entry from $\pi$ to obtain a $\beta$-avoiding permutation.