### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 6 |

Volume | 2003-66 |

Publication status | Published - 2003 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2003-66 |

### Fingerprint

### Keywords

- singularities
- matrices
- graphs

### Cite this

*Conditions for Singular Incidence Matrices*. (CentER Discussion Paper; Vol. 2003-66). Tilburg: Operations research.

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**Conditions for Singular Incidence Matrices.** / Haemers, W.H.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Conditions for Singular Incidence Matrices

AU - Haemers, W.H.

N1 - Pagination: 6

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - singularities

KW - matrices

KW - graphs

M3 - Discussion paper

VL - 2003-66

T3 - CentER Discussion Paper

BT - Conditions for Singular Incidence Matrices

PB - Operations research

CY - Tilburg

ER -