An Algorithm to List All the Fixed-Point Free Involutions on a Finite Set

A fixed-point free involution on a finite set S is defined as a bijection I : S S such as e S, I(I(e)) = e and e S, I(e) = e. In this article, the fixed-point free involutions are represented as partitions of the set S, and some properties linked to this representation are exhibited. Then an optimal algorithm to list all the fixed-point free involutions is presented. Its soundess 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 Algorithm, Fixed-point free involutions, Partitions, Recursion

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Cyril Prissette
• Keywords: CORR 2010, Education, Finite Set, Fixed-point Free Involutions, Optimal Algorithm