Almost avoiding permutations
Robert Brignall, Shalosh B. Ekhad, Rebecca Smith, and Vince Vatter

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: almost avoids if one can remove a single entry from to obtain a -avoiding permutation.
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