An involution on derangements preserving excedances and right-to-left minima

TL;DR

This paper provides a bijective proof linking derangements' parity and excedances, further refining the understanding by incorporating right-to-left minima.

Contribution

It introduces a bijective approach that preserves excedances and right-to-left minima, extending prior results on derangements' parity.

Findings

Established a bijection preserving excedances and minima

Refined previous parity results for derangements

Enhanced combinatorial understanding of derangement properties

Abstract

We give a bijective proof of a result by R.~Mantaci and F.~Rakotondrajao from 2003, regarding even and odd derangement with a fixed number of excedances. We refine this result by also considering the set of right-to-left minima.