Intersections and supports of quadruple systems

Charles J. Colbourn, Alan Hartman

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The possible intersection sizes for Steiner quadruple systems are examined. The determination of possible intersection sizes for v ≡ 4, 8 (mod 12), v ≥ 40, was recently completed by Lo Faro. For v ≡ 0 (mod 6), v ≥ 42, we solve completely the analogous intersection problem for threewise balanced designs with a spanning set of blocks of size 6, and blocks of size four otherwise. For v ≡ 2 (mod 12), v ≥ 38, we solve the intersection problem except when the intersection size is less than (v - 2)(v - 14)/6. For v ≡ 10 (mod 12), v ≥ 46, we solve the intersection problem except when the intersection size is less than (v - 10)/6. Using these results on intersection, we obtain substantial partial results on the possible support sizes of quadruple systems with λ = 2 and 3.

Original languageEnglish (US)
Pages (from-to)119-137
Number of pages19
JournalDiscrete Mathematics
Volume97
Issue number1-3
DOIs
StatePublished - Dec 10 1991
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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