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The Fine Intersection Problem for Steiner Triple Systems
"... Abstract. The intersection of two Steiner triple systems (X, A) and (X, B) is the set A ∩ B. The fine intersection problem for Steiner triple systems is to determine for each v, the set I(v), consisting of all possible pairs (m, n) such that there exist two Steiner triple systems of order v whose in ..."
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Abstract. The intersection of two Steiner triple systems (X, A) and (X, B) is the set A ∩ B. The fine intersection problem for Steiner triple systems is to determine for each v, the set I(v), consisting of all possible pairs (m, n) such that there exist two Steiner triple systems of order v whose
Steiner Triple Systems Intersecting in Pairwise Disjoint Blocks
 Electronic J. Combin
"... Two Steiner triple systems (X,A)and(X,B) are said to intersect in m pairwise disjoint blocks if A # B = m and all blocks in A#B are pairwise disjoint. For each v, we completely determine the possible values of m such that there exist two Steiner triple systems of order v intersecting in m pair ..."
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Cited by 5 (3 self)
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Two Steiner triple systems (X,A)and(X,B) are said to intersect in m pairwise disjoint blocks if A # B = m and all blocks in A#B are pairwise disjoint. For each v, we completely determine the possible values of m such that there exist two Steiner triple systems of order v intersecting in m
Quasiembeddings and intersections of latin squares of different orders
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 43 (2009), PAGES 197–209
, 2009
"... We consider a common generalization of the embedding and intersection problems for latin squares. Specifically, we extend the definition of embedding to squares whose sides do not meet the necessary condition for embedding and extend the intersection problem to squares of different orders. Results a ..."
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Cited by 1 (0 self)
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We consider a common generalization of the embedding and intersection problems for latin squares. Specifically, we extend the definition of embedding to squares whose sides do not meet the necessary condition for embedding and extend the intersection problem to squares of different orders. Results
5sparse Steiner triple systems
, 2005
"... Steiner triple systems are known to exist for orders n ≡ 1, 3 mod 6. 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 thesis resolves the problem of determining the spectrum ..."
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Steiner triple systems are known to exist for orders n ≡ 1, 3 mod 6. 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 thesis resolves the problem of determining
On 2ranks of Steiner triple systems
 Electron. J. Combin., 2:Research Paper
, 1995
"... Our main result is an existence and uniqueness theorem for Steiner triple systems which associates to every such system a binary code  called the "carrier"  which depends only on the order of the system and its 2rank. When the Steiner triple system is of 2rank less than the number ..."
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Our main result is an existence and uniqueness theorem for Steiner triple systems which associates to every such system a binary code  called the "carrier"  which depends only on the order of the system and its 2rank. When the Steiner triple system is of 2rank less than the number
Hamilton Decompositions Of BlockIntersection Graphs Of Steiner Triple Systems
 Ars Combinatoria
, 1996
"... Blockintersection graphs of Steiner triple systems are considered. We prove that the blockintersection graphs of nonisomorphic Steiner triple systems are themselves nonisomorphic. We also prove that each Steiner triple system of order at most 15 has a Hamilton decomposable blockintersection gra ..."
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Blockintersection graphs of Steiner triple systems are considered. We prove that the blockintersection graphs of nonisomorphic Steiner triple systems are themselves nonisomorphic. We also prove that each Steiner triple system of order at most 15 has a Hamilton decomposable blockintersection
Decomposing blockintersection graphs of Steiner triple systems into triangles
"... The problem of decomposing the block intersection graph of a Steiner triple system into triangles is considered. In the case when the block intersection graph has even degree, this is completely solved, while when the block intersection graph has odd degree, removal of some spanning subgraph of odd ..."
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The problem of decomposing the block intersection graph of a Steiner triple system into triangles is considered. In the case when the block intersection graph has even degree, this is completely solved, while when the block intersection graph has odd degree, removal of some spanning subgraph of odd
Solving large steiner triple covering problems
 Operations Research Letters
, 2011
"... Abstract Computing the 1width of the incidence matrix of a Steiner Triple System gives rise to small set covering instances that provide a computational challenge for integer programming techniques. One major source of difficulty for instances of this family is their highly symmetric structure, wh ..."
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Cited by 5 (1 self)
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, which impairs the performance of most branchandbound algorithms. The largest instance in the family that has been solved corresponds to a Steiner Tripe System of order 81. We present optimal solutions to the set covering problems associated with systems of orders 135 and 243. The solutions
Sets of Three Pairwise Orthogonal Steiner Triple Systems
, 2010
"... Two Steiner triple systems (STS) are orthogonal if their sets of triples are disjoint, and two disjoint pairs of points defining intersecting triples in one system fail to do so in the other. In 1994, it was shown [2] that there exist a pair of orthogonal Steiner triple systems of order v for all v ..."
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Two Steiner triple systems (STS) are orthogonal if their sets of triples are disjoint, and two disjoint pairs of points defining intersecting triples in one system fail to do so in the other. In 1994, it was shown [2] that there exist a pair of orthogonal Steiner triple systems of order v for all v
Results 1  10
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288