Quadruple systems containing AG(3,2)

Alan Hartman

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

Quadruple systems containing AG(3,2)

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

Access to Document

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

Cite this

@article{77171b80debf49479e206c5291c97e2c,

title = "Quadruple systems containing AG(3,2)",

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).",

author = "Alan Hartman",

year = "1982",

month = may,

doi = "10.1016/0012-365X(82)90151-0",

language = "English",

volume = "39",

pages = "293--299",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "3",

}

TY - JOUR

T1 - Quadruple systems containing AG(3,2)

AU - Hartman, Alan

PY - 1982/5

Y1 - 1982/5

N2 - 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).

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).

UR - http://www.scopus.com/inward/record.url?scp=0242532729&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(82)90151-0

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

M3 - Article

AN - SCOPUS:0242532729

SN - 0012-365X

VL - 39

SP - 293

EP - 299

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3

ER -

Quadruple systems containing AG(3,2)

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this