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Colouring of cubic graphs by Steiner triple systems
 JOURNAL OF COMBINATORIAL THEORY, SERIES B
, 2004
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Configurations and trades in Steiner
"... This is a preprint of an article accepted for publication in the Australasian Journal of Combinatorics c©2004 (copyright owner as specified in the journal). The main result of this paper is the determination of all pairwise nonisomorphic trade sets of volume at most 10 which can appear in Steiner t ..."
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triple systems. We also enumerate partial Steiner triple systems having at most 10 blocks as well as configurations with no points of degree 1 and tradeable configurations having at most 12 blocks. AMS classification: 05B07
ON STEINER LOOPS AND POWER ASSOCIATIVITY 217
"... Abstract. In this paper we investiagte Steiner loops introduced by N.S. Mendelsohn [Aeq. Math. 6 (1991), 228–230] and provide six (seven) equivalent identities to characterize it. We also prove the power associativity of Bol loops by using closure (Hexagonal) conditions. 1. Steiner loops In [9] Me ..."
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] Mendelsohn has defined the concept of a generalized triple system as follows. Let S be a set of ν elements. Let T be a collection of b subsets of S, each of which contains three elements arranged cyclically, and such that any ordered pair of elements of S appears in exactly a cyclic triplet (note the cyclic
Antipodal Triple Systems
 AUSTRALASIAN JOURNAL OF COMBINATORICS 9(1994). NN. B71&;1
, 1994
"... An antipodal triple system of order v is a triple (V, B, 1), where 1 V 1 = v, B is a set of cyclically oriented 3subsets of V, and f: V+ V is an involution with one fixed point such that: (i) (V, B U f(B)) is a Mendelsohn triple system. Oi) B n f(B) = 0. (iii) f is an isomorphism between the Stei ..."
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An antipodal triple system of order v is a triple (V, B, 1), where 1 V 1 = v, B is a set of cyclically oriented 3subsets of V, and f: V+ V is an involution with one fixed point such that: (i) (V, B U f(B)) is a Mendelsohn triple system. Oi) B n f(B) = 0. (iii) f is an isomorphism between
The Steiner Quadruple Systems of Order 16
"... Dedicated to the memory of Professor Jack van Lint 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 ..."
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groups and the structures of the derived Steiner triple systems of order 15—are tabulated. A doublecounting consistency check is carried out to gain confidence in the correctness of the classification.
Construction of extended Steiner systems for information retrieval
 Revista Matemática Complutense
, 2008
"... A multiset batch code is a variation of information retrieval where a tmultiset of items can be retrieved by reading at most one bit from each server. We study a problem at the other end of the spectrum, namely that of retrieving a tmultiset of items by accessing exactly one server. Our solution t ..."
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Cited by 3 (0 self)
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to the problem is a combinatorial notion called an extended Steiner system, which was first studied by Johnson and Mendelsohn [11]. An extended Steiner system ES(t, k, v) is a collection of kmultisets (thus, allowing repetition of elements in a block) of a vset such that every tmultiset belongs to exactly one
5sparse Steiner triple systems of order n exist for almost all admissible n
, 2005
"... Steiner triple systems are known to exist for orders n ≡ 1, 3 mod 6, the admissible orders. There are many known constructions for infinite classes of Steiner triple systems. However, Steiner triple systems that lack prescribed configurations are harder to find. This paper gives a proof that the spe ..."
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Steiner triple systems are known to exist for orders n ≡ 1, 3 mod 6, the admissible orders. There are many known constructions for infinite classes of Steiner triple systems. However, Steiner triple systems that lack prescribed configurations are harder to find. This paper gives a proof
Results 11  20
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519