Involutions and their progenies

Tewodros Amdeberhan, Victor H. Moll

Published 2014-06-09Version 1

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, asymptotic estimates as well as arithmetic and combinatorial properties.