# The Foata correspondence, cycle lengths and anomalies

## TL;DR

This paper demonstrates that the Foata correspondence serves as a bijection between two classes of permutations with equal cardinalities, addressing a question raised in the context of jammed configurations in theater models.

## Contribution

It establishes a new connection between permutation classes and the Foata correspondence, providing a bijective proof for their equal cardinalities.

## Key findings

- Foata correspondence acts as a bijection between the two permutation classes
- Addresses a question from the study of jammed configurations in theater models
- Provides a combinatorial interpretation of permutation class equivalences

## Abstract

In their study of the densest jammed configurations for theater models, Krapivsky and Luck observe that two classes of permutations have the same cardinalities and ask for a bijection between them. In this note we show that the Foata correspondence provides the desired bijection.