Journal of Combinatorics
Volume 6 (2015)
Involutions and their progenies
Pages: 483 – 508
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on the special class of involutions and their partial sums. The paper provides generating functions, determinantal expressions, and asymptotic estimates as well as arithmetic and combinatorial properties.