منابع مشابه
The existence of resolvable Steiner quadruple systems
A Steiner quadruple system of order v is a set X of cardinality v, and a set Q, of 4-subsets of X, called blocks, with the property that every 3-subset of X is contained in a unique block. A Steiner quadruple system is resolvable if Q can be partitioned into parallel classes (partitions of X). A necessary condition for the existence of a resolvable Steiner quadruple system is that v = 4 or 8 (m...
متن کاملClassification of Flag-Transitive Steiner Quadruple Systems
A Steiner quadruple system of order v is a 3 − (v, 4, 1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus solving the ”still open and longstanding problem of classifying all flag-transitive 3− (v, k,1) designs” (cf. [5, p. 273], [6]) for the smallest value o...
متن کاملThe Steiner quadruple systems of order 16
The Steiner quadruple systems of order 16 are classified up to isomorphism by means of an exhaustive computer search. The number of isomorphism classes of such designs is 1,054,163. Properties of the designs—including the orders of the automorphism groups and the structures of the derived Steiner triple systems of order 15—are tabulated. A double-counting consistency check is carried out to gai...
متن کاملAffine-invariant strictly cyclic Steiner quadruple systems
A Steiner quadruple system of order v, denoted by SQS(v), is a pair (V, B), where V is a finite set of v points, and B is a collection of 4-subsets of V , called blocks or quadruples, such that each 3-subset (triple) of V is contained in exactly one block in B. An automorphism group of SQS(v) is a permutation group on V leaving B invariant. An SQS(v) is said to be cyclic if it admits an automor...
متن کاملSmall Group Divisible Steiner Quadruple Systems
Melissa Keranen∗, Donald Kreher, Artem Zhuravlev, Michigan Technological University A group divisible Steiner quadruple system, is a triple (X,H,B) where X is a v-element set of points, H = {H1, H2, . . . , Hr} is a partition of X into holes and B is a collection of 4-element subsets of X called blocks such that every 3-element subset is either in a block or a hole but not both. We investigate ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90446-m