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
which acts on the finite set
A common task in computational group theory is to compute the orbit of some element
under G. At the same time, one can record a Schreier vector for
This vector can then be used to find an element
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 overview.
A Schreier vector for
is a vector
such that: Here we illustrate, using pseudocode, the use of Schreier vectors in two algorithms