Pairwise Balanced Designs with Prescribed Minimum Dimension

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 is a linear space on v points whose lines (or blocks) have sizes belonging to K . We show that, for...

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Bibliographic Details
Published in:Discrete & computational geometry 2014-03, Vol.51 (2), p.485-494
Main Authors: Dukes, Peter J., Ling, Alan C. H.
Format: Article
Language:English
Subjects:
Balancing
Combinatorics
Computational geometry
Computational mathematics
Computational Mathematics and Numerical Analysis
Geometry
Integers
Lower bounds
Mathematics
Mathematics and Statistics
Recall
Subspaces
Texts
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Summary: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 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 of dimension at least d for all sufficiently large and numerically admissible v .
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-013-9564-3