Small Group Divisible Steiner Quadruple Systems

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Small 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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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...

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Affine-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...

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Classification 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...

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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2008

ISSN: 1077-8926

DOI: 10.37236/764