Minimal transitive products of transpositions—the reconstruction of a proof of A. Hurwitz. (English) Zbl 0886.05006

Strehl, Volker

Sémin. Lothar. Comb. 37, B37c, 12 p. (1996).

Summary: We want to draw the combintorialists’ attention to an important, but apparently little known paper by the function theorist A. Hurwitz, published in 1891, where he announces the solution of a counting problem which has gained some attention recently: in how many ways can a given permutation be written as the product of transpositions such that the transpositions generate the full symmetric group, and such that the number of factors is as small as possible (under this side condition).

MSC:

05A15	Exact enumeration problems, generating functions
05A05	Permutations, words, matrices

Keywords:

counting problem; permutation; transpositions; symmetric group