What type of study is this?

This is a Quantitative Study study.

synapse

⌘+K

synapse

⌘+K

October 21, 2025Open Access

Pattern Avoidance and the Fundamental Bijection

Key Points

Permutations avoiding a specific pattern are enumerated, along with their transformations under the fundamental bijection.
The research identifies permutations in the symmetric group that maintain pattern avoidance through multiple iterations.
Understanding the relationship between original and transformed permutations provides insights into their structural properties.
Future studies are suggested to explore additional patterns and properties of permutations under bijections.

Abstract

The fundamental bijection is a bijection: Sₙₙ in which one uses the standard cycle form of one permutation to obtain another permutation in one-line form. In this paper, we enumerate the set of permutations ₙ that avoids a pattern ₃, whose image () also avoids. We additionally consider what happens under repeated iterations of ; in particular, we enumerate permutations ₙ that have the property that and its first k iterations under all avoid a pattern. Finally, we consider permutations with the property that =² () that avoid a given pattern, and end the paper with some directions for future study.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper