On the existence of cyclic Steiner Quadruple systems SQS (2p)
نویسندگان
چکیده
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 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 کاملOn orthogonal resolutions of the classical Steiner quadruple system SQS(16)
A Steiner quadruple system SQS(16) is a pair (V,B) where V is a 16-set of objects and B is a collection of 4-subsets of V , called blocks, so that every 3-subset of V is contained in exactly one block. By classical is meant the boolean quadruple system, also known as the affine geometry AG(4,2). A parallel class is a collection of four blocks which partition V . The system possesses a resolutio...
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 کاملOn the Existence of Certain Steiner Systems
In this paper we prove the existence of certain Steiner systems. The results of this paper are divided into three sections: In section 1, we investigate Steiner systems of type S(3, 4, 8). In section 2, we study Steiner systems of type S(5, 6, 12), and in the last section we study Steiner systems of type (5, 8, 24), the MOG and the Hexacode. Mathematics Subject Classification: 20C15, 20E28
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90452-8