Comparing the expected number of random elements from the symmetric and the alternating groups needed to generate a transitive subgroup - Lucchini, Andrea (Ars mathematica contemporanea, 2019)
Given a transitive permutation group of degree ?$n$?, we denote by ?$e_{τ}(G)$? the expected number of elements of ?$G$? which have to be drawn at random, with replacement, before a set of generators of a transitive subgroup of ?$G$? is found. We compare ?$e_{τ}(Sym(n))$? and ?$e_{τ}(Alt(n))$?.
Keywords: expectation; generation; generiranje; pričakovanje; transitive groups; tranzitivne grupe