$2\,000\,000$ Steiner triple systems of order $19$
نویسندگان
چکیده
منابع مشابه
The Steiner triple systems of order 19
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. There are three main parts of the classification: constructing an initial set of blocks, the seed...
متن کاملA Catalogue of the Steiner Triple Systems of Order 19
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.
متن کاملProperties of the Steiner Triple Systems of Order 19
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 chromatic index 10, except for 4 075 designs with chromatic index 11 and two with chromatic inde...
متن کاملSteiner Triple Systems of Order 19 with Nontrivial Automorphism Group
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 use of tactical configurations in conjunction with orderly algorithms underlies practical techniques for the generation of the designs, and the subexponential time isomorphism technique for triple systems is improved in pract...
متن کاملSteiner Triple Systems of Order 19 Contain a Subsystem of Order
In this paper, we enumerate the (nonisomorphic) Steiner triple systems of order 19 which contain a subsystem of order 9. The number of these designs is precisely 284457. We also determine which of these designs also contain at least one subsystem of order 7, and how many. Exactly 13529 of them contain at least one subsystem of order 7.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1985
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1985-0777284-3