Conditions for Singular Incidence Matrices

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages6
Volume2003-66
Publication statusPublished - 2003

Publication series

NameCentER Discussion Paper
Volume2003-66

Keywords

  • singularities
  • matrices
  • graphs

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