A limit theorem for the six-length of random functional graphs with a fixed degree sequence (Q2278111)

Summary: We obtain results on the limiting distribution of the six-length of a random functional graph, also called a functional digraph or random mapping, with given in-degree sequence. The six-length of a vertex \(v\in V\) is defined from the associated mapping, \(f:V\to V\), to be the maximum \(i\in V\) such that the elements \(v, f(v), \ldots, f^{i-1}(v)\) are all distinct. This has relevance to the study of algorithms for integer factorisation.