Schreier Vector (Paperback)

PMHigh Quality Content by WIKIPEDIA articles! In mathematics, especially the field of computational group theory, a Schreier vector is a tool for reducing the time and space complexity required to calculate orbits of a permutation group. Suppose G is a finite group with generating sequence X = {x1,x2,...,xr} which acts on the finite set = {1,2,...,n}. A common task in computational group theory is to compute the orbit of some element omega in Omega under G. At the same time, one can record a Schreier vector for . This vector can then be used to find the g in G satisfying g = , for any alpha in omega^G. Use of Schreier vectors to perform this requires less storage space and time complexity than storing these g explicitly. All variables used here are defined in the overvie