Quadruple systems containing AG(3,2)

Alan Hartman

doi:10.1016/0012-365X(82)90151-0

Quadruple systems containing AG(3,2)

Alan Hartman

Research output: Contribution to journal › Article › peer-review

Abstract

A quadruple system of order v, denoted QS(v) is an ordered pair (X, Q) where X is a set of cardinality v and Q is a set of 4-subsets of X called blocks, with the property that every 3-subset of X is contained in a unique block. The points and planes of the affine geometry AG(3, 2) form a QS(8). We prove that a QS(v) containing a proper subsystem isomorphic to AG(3, 2) exists if and only if v≥16 and v≡2 or 4 (mod 6).

Original language	English
Pages (from-to)	293-299
Number of pages	7
Journal	Discrete Mathematics
Volume	39
Issue number	3
DOIs	https://doi.org/10.1016/0012-365X(82)90151-0
State	Published - May 1982
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(82)90151-0

Cite this

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AB - A quadruple system of order v, denoted QS(v) is an ordered pair (X, Q) where X is a set of cardinality v and Q is a set of 4-subsets of X called blocks, with the property that every 3-subset of X is contained in a unique block. The points and planes of the affine geometry AG(3, 2) form a QS(8). We prove that a QS(v) containing a proper subsystem isomorphic to AG(3, 2) exists if and only if v≥16 and v≡2 or 4 (mod 6).

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Quadruple systems containing AG(3,2)

Abstract

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