The largest and the smallest fixed points of permutations
Combinatorics
2009-04-21 v1
Abstract
We give a new interpretation of the derangement numbers d_n as the sum of the values of the largest fixed points of all non-derangements of length n-1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We provide analytic and bijective proofs of both results, as well as a new recurrence for the derangement numbers.
Cite
@article{arxiv.0904.2792,
title = {The largest and the smallest fixed points of permutations},
author = {Emeric Deutsch and Sergi Elizalde},
journal= {arXiv preprint arXiv:0904.2792},
year = {2009}
}
Comments
7 pages