Enumerating Steiner triple systems

被引：1

作者：

Heinlein, Daniel ^{[1
,2
]}

Ostergard, Patric R. J. ^{[1
]}

机构：

[1] Aalto Univ, Sch Elect Engn, Dept Informat & Commun Engn, Aalto, Finland

[2] Aalto Univ, Sch Elect Engn, Dept Informat & Commun Engn, POB 15400, Aalto 00076, Finland

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2023年 / 31卷 / 10期

基金：

芬兰科学院;

关键词：

classification; counting; regular graph; Steiner triple system; FAST GENERATION; LATIN SQUARES; ORDER; 21; GRAPHS;

D O I：

10.1002/jcd.21906

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes. Computational approaches for counting STSs are here considered and lead to an algorithm that is used to obtain the number of isomorphism classes for order 21: 14,796,207,517,873,771.

引用

页码：479 / 495

页数：17

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