On the dimension of Kirichenko space

Abstract

We introduce a notion of the Kirichenko space which is connected with the notion of Gorenstein matrix (see [2], ch. 14). Every element of Kirichenko space is an n × n matrix, whose elements are solutions of the equations ai,j +aj,σ(i) = ai,σ(i) ; a₁,i = 0 for i, j = 1, . . . , n determined by a permutation σ which has no cycles of the length 1. We give a formula for the dimension of this space in terms of the cyclic type of σ.