Pairwise Balanced Designs with Prescribed Minimum Dimension

Discrete & Computational Geometry - Tập 51 - Trang 485-494 - 2013
Peter J. Dukes1, Alan C. H. Ling2
1Department of Mathematics and Statistics, University of Victoria, Victoria, Canada
2Department of Computer Science, University of Vermont, Burlington, USA

Tóm tắt

The dimension of a linear space is the maximum positive integer d such that any d of its points generate a proper subspace. For a set K of integers at least two, recall that a pairwise balanced design $\operatorname{PBD}(v,K)$ is a linear space on v points whose lines (or blocks) have sizes belonging to K. We show that, for any prescribed set of sizes K and lower bound d on the dimension, there exists a $\operatorname{PBD}(v,K)$ of dimension at least d for all sufficiently large and numerically admissible v.

Tài liệu tham khảo

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