Premium
A small basis for four‐line configurations in steiner triple systems. Dedicated to the memory of gemma holly griggs
Author(s) -
Grannell M. J.,
Griggs T. S.,
Mendelsohn E.
Publication year - 1995
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.3180030107
Subject(s) - gemma , line (geometry) , mathematics , steiner system , combinatorics , order (exchange) , geometry , botany , finance , economics , biology
Formulae for the numbers of two, three, and four‐line configurations in a Steiner triple system of order v , STS( v ), are given. While the formulae for two and three‐line configurations depend only on v , the same is true for only 5 of the 16 four‐line configurations. For the other 11 and fixed v , the number of occurrences of any one of them, in particular the Pasch configuration, determines the number of occurrences of all the others. © 1995 John Wiley & Sons, Inc.