An Algorithm to List All the Fixed-Point Free Involutions on a Finite Set
Data Structures and Algorithms
2010-07-26 v1
Abstract
An involution on a finite set is a bijection such as I(I(e))=e for all the element of the set. A fixed-point free involution on a finite set is an involution such as I(e)=e for none element of the set. In this article, the fixed-point free involutions are represented as partitions of the set and some properties linked to this representation are exhibited. Then an optimal algorithm to list all the fixed-point free involutions is presented. Its soundness relies on the representation of the fixed-point free involutions as partitions. Finally, an implementation of the algorithm is proposed, with an effective data representation.
Keywords
Cite
@article{arxiv.1006.3993,
title = {An Algorithm to List All the Fixed-Point Free Involutions on a Finite Set},
author = {Cyril Prissette},
journal= {arXiv preprint arXiv:1006.3993},
year = {2010}
}