A simple bijective proof of a familiar derangement recurrence
Combinatorics
2020-05-25 v1
Abstract
It is well known that the derangement numbers , which count permutations of length with no fixed points, satisfy the recurrence for . Combinatorial proofs of this formula have been given by Remmel, Wilf, D\'esarm\'enien and Benjamin--Ornstein. Here we present yet another, arguably simpler, bijective proof.
Cite
@article{arxiv.2005.11312,
title = {A simple bijective proof of a familiar derangement recurrence},
author = {Sergi Elizalde},
journal= {arXiv preprint arXiv:2005.11312},
year = {2020}
}