TL;DR: With any permutation g of a set @W is associated a partition of @W into the cycles of g, and what information do the authors get about a group G of permutations if they know either the set or the multiset of partitions of@W, or of partitions which arise as the cycle partitions of its elements?
TL;DR: In this article, the Parker vector of a permutation group is defined as a sequence of natural numbers enumerating the orbits of the actions of G on the set of cycles appearing in its elements.