Steiner Triple Systems of Order 21 with a Transversal Subdesign TD(3,6)

Steiner Triple Systems of Order 21 with a Transversal Subdesign TD(3,6) Full article

Journal

Problems of Information Transmission
ISSN: 0032-9460 , E-ISSN: 1608-3253

Output data

Year: 2020, Volume: 56, Number: 1, Pages: 23-32 Pages count : 10 DOI: 10.1134/s0032946020010032

Tags

Steiner triple system, subdesign, transversal design, Latin square

Authors

Guan Y. ¹ , Shi M.J. ¹ , Krotov D.S. ²

Affiliations

1	Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui Province, P. R. China
2	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

A Steiner triple system (STS) contains a transversal subdesign TD(3,w) if its point set has three pairwise disjoint subsets A, B, C of size w and w2 blocks of the STS intersect with each of A, B, C (those w^2 blocks form a TD(3,w)). We prove several structural properties of Steiner triple systems of order 3w+3 that contain one or more transversal subdesigns TD(3, w). Using exhaustive search, we find that there are 2 004 720 isomorphism classes of STS(21) containing a subdesign TD(3,6) (or, equivalently, a 6-by-6 Latin square).

Guan Y. , Shi M.J. , Krotov D.S.
Steiner Triple Systems of Order 21 with a Transversal Subdesign TD(3,6)
Problems of Information Transmission. 2020. V.56. N1. P.23-32. DOI: 10.1134/s0032946020010032 WOS Scopus РИНЦ OpenAlex

Гуань Ю. , Ши М. , Кротов Д.С.
Системы троек Штейнера порядка 21 с трансверсальным поддизайном TD(3,6)
Проблемы передачи информации. 2020. Т.56. №1. С.26-37. DOI: 10.31857/S0555292320010039 РИНЦ OpenAlex

Submitted:	May 20, 2019
Accepted:	Aug 29, 2019
Published online:	Apr 16, 2020

Web of science:	WOS:000526343800003
Scopus:	2-s2.0-85083506599
Elibrary:	43284070
OpenAlex:	W3105490101

DB	Citing
Web of science	2
Scopus	2
Elibrary	2
OpenAlex	2