Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs

E.R. van Dam, E. Spence

Research output: Working paperDiscussion paperOther research output

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Abstract

In this and a sequel paper [10] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize 2-(v, k, É) designs, and include partial geometric designs and uniform multiplicative designs.Here we study the latter, which are precisely the nonsingular designs.We classify all such designs with smallest singular value at most, generalize the Bruck-Ryser-Chowla conditions, and enumerate, partly by computer, all uniform multiplicative designs on at most 30 points.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages15
Volume2003-67
Publication statusPublished - 2003

Publication series

NameCentER Discussion Paper
Volume2003-67

Fingerprint

Combinatorial Design
Singular Values
Multiplicative
Geometric Design
Generalise
Incidence Matrix
Classify
Design
Distinct
Partial

Keywords

  • combinatorics
  • matrices
  • singularities

Cite this

van Dam, E. R., & Spence, E. (2003). Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs. (CentER Discussion Paper; Vol. 2003-67). Tilburg: Operations research.
van Dam, E.R. ; Spence, E. / Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs. Tilburg : Operations research, 2003. (CentER Discussion Paper).
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van Dam, ER & Spence, E 2003 'Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs' CentER Discussion Paper, vol. 2003-67, Operations research, Tilburg.

Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs. / van Dam, E.R.; Spence, E.

Tilburg : Operations research, 2003. (CentER Discussion Paper; Vol. 2003-67).

Research output: Working paperDiscussion paperOther research output

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T1 - Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs

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AU - Spence, E.

N1 - Pagination: 15

PY - 2003

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N2 - In this and a sequel paper [10] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize 2-(v, k, É) designs, and include partial geometric designs and uniform multiplicative designs.Here we study the latter, which are precisely the nonsingular designs.We classify all such designs with smallest singular value at most, generalize the Bruck-Ryser-Chowla conditions, and enumerate, partly by computer, all uniform multiplicative designs on at most 30 points.

AB - In this and a sequel paper [10] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize 2-(v, k, É) designs, and include partial geometric designs and uniform multiplicative designs.Here we study the latter, which are precisely the nonsingular designs.We classify all such designs with smallest singular value at most, generalize the Bruck-Ryser-Chowla conditions, and enumerate, partly by computer, all uniform multiplicative designs on at most 30 points.

KW - combinatorics

KW - matrices

KW - singularities

M3 - Discussion paper

VL - 2003-67

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BT - Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs

PB - Operations research

CY - Tilburg

ER -

van Dam ER, Spence E. Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs. Tilburg: Operations research. 2003. (CentER Discussion Paper).