Journal of Combinatorics

Volume 6 (2015)

Number 4

Involutions and their progenies

Pages: 483 – 508

DOI: http://dx.doi.org/10.4310/JOC.2015.v6.n4.a5

Authors

Tewodros Amdeberhan (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Victor Moll (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Abstract

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.

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Published 31 July 2015