Title

Counting configurations in designs

Document Type

Article

Publication Date

2001

Publication Title

Journal of Combinatorial Theory, Series A

Department

Mathematics and Computer Science

Abstract

Given a t-(v, k, ?) design, form all of the subsets of the set of blocks. Partition this collection of configurations according to isomorphism and consider the cardinalities of the resulting isomorphism classes. Generalizing previous results for regular graphs and Steiner triple systems, we give linear equations relating these cardinalities. For any fixed choice of t and k, the coefficients in these equations can be expressed as functions of v and ? and so depend only on the design's parameters, and not its structure. This provides a characterization of the elements of a generating set for m-line configurations of an arbitrary design.

Volume

96

Issue

2

pp.

341-357

ISSN

0097-3165