Computation of the Kramer-Mesner matrix

The Kramer-Mesner matrix of a t-(v, k, lambda) is a modified incidence matrix between the t-subsets and the k-subsets of the point set V={1, ..., v}. Here the prescribed group comes into play - the details are described on this page - because we only consider the incidences between the orbits of the group on the t-subsets and the orbits of the group on the k-subsets of V.

In order to compute a Kramer-Mesner matrix for a given admissible parameter set t-(v, k, lambda), you have to press the button "Kramer-Mesner" to receive the table

Here you can choose some options for the calculation (very sensible is the choice of "canonical representatives") and then start the computation by pressing "compute Kramer Mesner matrix". The computation (it runs on your terminal) is finished by the remark "LADDER_INFO closed". If you want to have a look on the matrix, press "Kramer-Mesner" and "show matrix".

The Kramer-Mesner matrix for the parameter set 2-(15, 3, 1) for example is the following (the first row gives the dimensions of the matrix: 13x46):

13 46

3 3 1 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 3 1 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 2 2 0 2 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 2 1 2 2 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 1 1 1 0 0 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 4 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 2 1 0 1 1 1 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 2 1 0 1 1 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 1 2 2 1 2

Warning: if you have a small group, for example a cyclic group on a quite large number of points, the Kramer-Mesner matrix can be too big for the computation!

Remark: You have to click on the pictures to get them largely.

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Last updated: August 24, 1999, Evi Haberberger