Embedding partial geometries in Steiner designs

Authors

Andries Brouwer
Willem Haemers
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

1997

Abstract

We consider the following problem: given a partial geometry with v points and k points on a line, can one add to the line set a set of k-subsets of points such that the extended family of k-subsets is a 2-(v, k;, 1) design (or a Steiner system S(2, k, v)). We give some necessary conditions for such embeddings and several examples. One of these is an embedding of the partial geometry PQ⁺(7,2) into a 2-(120,8,1) design.

Publisher's Statement

Copyright Cambridge University Press 1997. Publisher’s version of record: https://doi.org/10.1017/CBO9780511526114.006

Publication Title

Geometry, Combinatorial Designs and Related Structures

Recommended Citation

Brouwer, A., Haemers, W., & Tonchev, V. (1997). Embedding partial geometries in Steiner designs. Geometry, Combinatorial Designs and Related Structures, 33-42. http://doi.org/10.1017/CBO9780511526114.006
Retrieved from: https://digitalcommons.mtu.edu/math-fp/151