An application of a bijection of Mansour, Deng, and Du

TL;DR

This paper demonstrates that large Schroder numbers count permutations whose reversed left-to-right minima decomposition is 321-avoiding, using the Mansour-Deng-Du bijection to connect permutations and Dyck paths.

Contribution

It introduces a new combinatorial interpretation of large Schroder numbers via a specific permutation class and employs the Mansour-Deng-Du bijection in this context.

Findings

Large Schroder numbers count permutations with reversed left-to-right minima decomposition being 321-avoiding.

The Mansour-Deng-Du bijection effectively links these permutations to Dyck paths.

The approach provides a new perspective on pattern-avoiding permutations.

Abstract

The large Schroder numbers are known to count several classes of permutations avoiding two 4-letter patterns. Here we show they count another family of permutations, those whose left to right minima decomposition, when reversed, is 321-avoiding. The main tool is the Mansour-Deng-Du bijection from 321-avoiding permutations to Dyck paths.