A small basis for four‐line configurations in steiner triple systems. Dedicated to the memory of gemma holly griggs | Zendy

Grannell M. J. | Zendy; Griggs T. S. | Zendy; Mendelsohn E. | Zendy

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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.

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