@techreport{df3b9bc52d63485d9322478f45e2b764,

title = "Conditions for Singular Incidence Matrices",

abstract = "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.",

keywords = "singularities, matrices, graphs",

author = "W.H. Haemers",

note = "Pagination: 6",

year = "2003",

language = "English",

volume = "2003-66",

series = "CentER Discussion Paper",

publisher = "Operations research",

type = "WorkingPaper",

institution = "Operations research",

}