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Properties of the Steiner triple systems of order 19
, 2010
"... Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5sparse, but no 6sparse, STS(19); there is exactly one uniform STS(19); there are exactly two STS(19) with no almost parallel classes; all STS(19) have chromatic number 3; all have ..."
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Cited by 4 (1 self)
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Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5sparse, but no 6sparse, STS(19); there is exactly one uniform STS(19); there are exactly two STS(19) with no almost parallel classes; all STS(19) have chromatic number 3; all
THE STEINER TRIPLE SYSTEMS OF ORDER 19
, 2004
"... Using an orderly algorithm, the Steiner triple systems of order 19 are classified; there are 11,084,874,829 pairwise nonisomorphic such designs. For each design, the order of its automorphism group and the number of Pasch configurations it contains are recorded; 2,591 of the designs are antiPasch. ..."
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Cited by 25 (7 self)
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Using an orderly algorithm, the Steiner triple systems of order 19 are classified; there are 11,084,874,829 pairwise nonisomorphic such designs. For each design, the order of its automorphism group and the number of Pasch configurations it contains are recorded; 2,591 of the designs are anti
A Catalogue of the Steiner Triple Systems of Order 19
"... Amethod for compressing Steiner triple systems is presented. This method has been used to compress the 11,084,874,829 Steiner triple systems of order 19 into approximately 39 gigabytes of memory. The compressed data can be obtained by contacting the authors. 1 ..."
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Cited by 2 (1 self)
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Amethod for compressing Steiner triple systems is presented. This method has been used to compress the 11,084,874,829 Steiner triple systems of order 19 into approximately 39 gigabytes of memory. The compressed data can be obtained by contacting the authors. 1
A catalogue of the Steiner triple . . .
"... A method for compressing Steiner triple systems is presented. This method has been used to compress the 11,084,874,829 Steiner triple systems of order 19 into approximately 39 gigabytes of memory. The compressed data can be obtained by contacting the authors. ..."
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A method for compressing Steiner triple systems is presented. This method has been used to compress the 11,084,874,829 Steiner triple systems of order 19 into approximately 39 gigabytes of memory. The compressed data can be obtained by contacting the authors.
Steiner Triple Systems of Order 19 and 21 with Subsystems of Order 7
"... Steiner triple systems (STSs) with subsystems of order 7 are classi ed. For order 19, this classi cation is complete, but for order 21 it is restricted to Wilsontype systems, which contain three subsystems of order 7 on disjoint point sets. The classi ed STSs of order 21 are tested for resolv ..."
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Cited by 4 (3 self)
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Steiner triple systems (STSs) with subsystems of order 7 are classi ed. For order 19, this classi cation is complete, but for order 21 it is restricted to Wilsontype systems, which contain three subsystems of order 7 on disjoint point sets. The classi ed STSs of order 21 are tested
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
Steiner Triple Systems of Order 19 with Nontrivial Automorphism Group
 Math. Comp
, 2003
"... There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed. ..."
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Cited by 6 (1 self)
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There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed.
The Cycle Switching Graph of the Steiner Triple Systems of Order 19 is Connected
 GRAPHS AND COMBINATORICS
"... Switching is a local transformation that when applied to a combinatorial object gives another object with the same parameters. It is here shown that the cycle switching graph of the 11 084 874 829 isomorphism classes of Steiner triple systems of order 19 as well as the cycle switching graph of the ..."
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Switching is a local transformation that when applied to a combinatorial object gives another object with the same parameters. It is here shown that the cycle switching graph of the 11 084 874 829 isomorphism classes of Steiner triple systems of order 19 as well as the cycle switching graph of the
The 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 t ..."
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Cited by 6 (2 self)
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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
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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≡ 1, 3 (mod 6), with v ≥ 7, v 6 = 9. In this paper we show that there exist three pairwise orthogonal Steiner triple systems of order v for all v ≡ 1 (mod 6), with v ≥ 19 and for all v ≡ 3 (mod 6), with v ≥ 27 with only 24 possible exceptions. 1 1
Results 1  10
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