English

A simple bijective proof of a familiar derangement recurrence

Combinatorics 2020-05-25 v1

Abstract

It is well known that the derangement numbers dnd_n, which count permutations of length nn with no fixed points, satisfy the recurrence dn=ndn1+(1)nd_n=nd_{n-1}+(-1)^n for n1n\ge1. 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.

Keywords

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}
}