Fischer-Clifford matrices of B(2, n)

Abstract

In [3] Almestady has presented a combinatorial method for constructing the Fischer-Clifford matrices of the generalized symmetric groups B(m, n), where m and n are positive integers. As a few examples for small values of m and n show, the manual calculation of these matrices presents formidable problems and hence a computerised approach to this combinatorial method is necessary. For this reason we have developed a series of computer programmes, written in GAP [7], that give various parameters of the Fischer-Clifford matrices of B(m, n). These programmes have been used in the development of the main programme that computes matrices which are row equivalent to the Fischer-Clifford matrices of B(2, n).

Keywords: Generalized symmetric group, m-compositions, Fischer-Clifford matrices, split extension

Quaestiones Mathematicae 29(2005), 9–37