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Properties of the Steiner triple systems of order 19

by Charles J. Colbourn, Anthony D. Forbes, Mike J. Grannell, Terry S. Griggs, Petteri Kaski, Patric R. J. Östergård, David A. Pike, Olli Pottonen , 2010
"... Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5-sparse, but no 6-sparse, 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 ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5-sparse, but no 6-sparse, 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

by Petteri Kaski, Patric R. J. Östergård , 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 anti-Pasch. ..."
Abstract - Cited by 25 (7 self) - Add to MetaCart
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

by Petteri Kaski, Patric R. J. Östergård, Olli Pottonen, Lasse Kiviluoto
"... 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 ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
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 . . .

by Petteri Kaski, Patric R. J. Östergård, Olli Pottonen, Lasse Kiviluoto
"... 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. ..."
Abstract - Add to MetaCart
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

by Petteri Kaski, Patric R. J. Östergård, Svetlana Topalova, Rosen Zlatarski
"... 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 Wilson-type systems, which contain three subsystems of order 7 on disjoint point sets. The classi ed STSs of order 21 are tested for resolv ..."
Abstract - Cited by 4 (3 self) - Add to MetaCart
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 Wilson-type 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

by L. D. Andersen, A. J. W. Hilton, E. Mendelsohn - 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 missing-edge 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 ..."
Abstract - Cited by 8 (1 self) - Add to MetaCart
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 missing-edge 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

by Charles J. Colbourn, Spyros S. Magliveras, D.R. Stinson - 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. ..."
Abstract - Cited by 6 (1 self) - Add to MetaCart
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

by Petteri Kaski, et al. - 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

by Petteri Kaski , Patric R. J. Österg̊ard , Olli Pottonen
"... 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 ..."
Abstract - Cited by 6 (2 self) - Add to MetaCart
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

by J. H. Dinitz, P. Dukes, Alan C. H. Ling , 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
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