On the dimension of Kirichenko space

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 $n\times n$ matrix, whose elements are solutions of the equations $a_{i,j}+a_{j,\sigma (i)} =a_{i,\sigma(i)}$; $a_{1,i}=0$ for $i,j =1,\ldots, n$ determined by a permutation $\sigma$ 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 $\sigma$.