Suppose one looks for a square integral matrixN, for which NN has a prescribed form.Then the Hasse-Minkowski invariants and the determinant of NN lead to necessary conditions for existence.The Bruck-Ryser-Chowla theorem gives a famous example of such conditions in case N is the incidence matrix of a square block design.This approach fails when N is singular.In this paper it is shown that in some cases conditions can still be obtained if the kernels of N and N are known, or known to be rationally equivalent.This leads for example to non-existence conditions for selfdual generalised polygons, semi-regular square divisible designs and distance-regular graphs.
|Place of Publication||Tilburg|
|Number of pages||6|
|Publication status||Published - 2003|
|Name||CentER Discussion Paper|