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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
Bicoloring Steiner Triple Systems
 Electron. J. Combin
, 1999
"... A Steiner triple system has a bicoloring with m color classes if the points are partitioned into m subsets and the three points in every block are contained in exactly two of the color classes. In this paper we give necessary conditions for the existence of a bicoloring with 3 color classes and give ..."
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Cited by 8 (1 self)
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A Steiner triple system has a bicoloring with m color classes if the points are partitioned into m subsets and the three points in every block are contained in exactly two of the color classes. In this paper we give necessary conditions for the existence of a bicoloring with 3 color classes
Perfect countably infinite Steiner triple systems
"... Perfect countably infinite Steiner triple systems ..."
Configurations and trades in Steiner triple systems
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 29 (2004), PAGES 75–84
, 2004
"... 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 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 co ..."
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Cited by 6 (2 self)
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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 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
Embedding partial Steiner triple systems
 Proc. London Math. Soc
, 1980
"... We prove that a partial Steiner triple system 8 of order n can be embedded in a Steiner triple system T of any given admissible order greater than 4w. Furthermore, if G(S), the missingedge graph of S, has the property that A(G)<ri(n + l)l and \E(G)\ then # can be embedded in a Steiner triple sys ..."
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Cited by 8 (1 self)
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We prove that a partial Steiner triple system 8 of order n can be embedded in a Steiner triple system T of any given admissible order greater than 4w. Furthermore, if G(S), the missingedge graph of S, has the property that A(G)<ri(n + l)l and \E(G)\ then # can be embedded in a Steiner triple
On 6sparse Steiner triple systems
 JOURNAL OF COMBINATORIAL THEORY, SERIES A
, 2006
"... We give the first known examples of 6sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6sparse systems for an infinite set of orders. Obs ..."
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Cited by 13 (2 self)
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We give the first known examples of 6sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6sparse systems for an infinite set of orders
Complete arcs in Steiner triple systems
"... A complete arc in a design is a set of elements which contains no block, and is maximal with respect to this property. The spectrum of sizes of complete arcs in Steiner triple systems is determined without exception here. ..."
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A complete arc in a design is a set of elements which contains no block, and is maximal with respect to this property. The spectrum of sizes of complete arcs in Steiner triple systems is determined without exception here.
Steiner Triple Systems and Perfect Codes
"... Using a computer implementation, we will show that there are perfect codes of length 15, generating Steiner triple systems which have rank 15. We will also show a strong connection between the rank/kernel of a perfect code and its systematics. Finally, we describe a method that will generate a perfe ..."
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Cited by 2 (0 self)
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Using a computer implementation, we will show that there are perfect codes of length 15, generating Steiner triple systems which have rank 15. We will also show a strong connection between the rank/kernel of a perfect code and its systematics. Finally, we describe a method that will generate a
Independent sets in Steiner triple systems
 Ars Comb
"... This is a preprint of an article accepted for publication in Ars Combinatoria c○2004 (copyright owner as specified in the journal). A set of points in a Steiner triple system (STS(v)) is said to be independent if no three of these points occur in the same block. In this paper we derive for each k ≤ ..."
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Cited by 2 (1 self)
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This is a preprint of an article accepted for publication in Ars Combinatoria c○2004 (copyright owner as specified in the journal). A set of points in a Steiner triple system (STS(v)) is said to be independent if no three of these points occur in the same block. In this paper we derive for each k
Caps and colouring Steiner triple systems
 Des. Codes Cryptogr
, 1998
"... Abstract. Hill [6] showed that the largest cap in PG(5, 3) has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 in AG(5, 3). Here we show that the size of a cap in AG(5, 3) is bounded above by 48. We also give an example of three disjoint 45caps in AG(5, 3). Using thes ..."
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Cited by 2 (0 self)
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these two results we are able to prove that the Steiner triple system AG(5, 3) is 6chromatic, and so we exhibit the first specific example of a 6chromatic Steiner triple system.
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