Mixing and covering in the symmetric groups
The covering of symmetric and alternating groups by powers of conjugacy classes is studied in this paper. Particular emphasis is laid on mixing which means that the computation of the powers is viewed as a stochastic process by taking samples out of the conjugacy class and then multiply them. In particular, the conjugacy class \([2^{n/2}]\) of the symmetric group \(S_n\) is studied; some new character identities are derived from the computation of \([2^{n/2}]^2\), also the power \([2^{n/2}]^3\) is computed. The results are applied to a certain classification of \(3\)-colored \(3\)-regular graphs.
scientific article; zbMATH DE number 1218710
scientific article