منابع مشابه
Strict colorings of Steiner triple and quadruple systems: a survey
The paper surveys problems, results and methods concerning the coloring of Steiner Triple and Quadruple Systems viewed as mixed hypergraphs. In this setting, two types of conditions are considered: each block of the Steiner system in question has to contain (i) a monochromatic pair of vertices, or, more restrictively, (ii) a triple of vertices that meets precisely two color classes.
متن کاملThe 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 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 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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1978
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90122-x