Name
Title | ||
|---|---|---|
An existence theory for pairwise balanced designs, III: Proof of the existence conjectures |
Abstract | ||
|---|---|---|
Given positive integers k and λ, balanced incomplete block designs on v points with block size k and index λ exist for all sufficiently large integers v satisfying the congruences λ(v − 1) ≡ 0 (mod k − 1) and λv(v − 1) ≡ 0 (mod k(k − 1)). Analogous results hold for pairwise balanced designs where the block sizes come from a given set K of positive integers. We also observe that the number of nonisomorphic designs on v points with given block size k > 2 and index λ tends to infinity as v increases (subject to the above congruences). |
Year | DOI | Venue |
|---|---|---|
1975 | 10.1016/0097-3165(75)90067-9 | Journal of Combinatorial Theory, Series A |
Field | DocType | Volume |
Integer,Block size,Discrete mathematics,Pairwise comparison,Combinatorics,Infinity,Congruence relation,Mathematics | Journal | 18 |
Issue | ISSN | Citations |
1 | 0097-3165 | 54 |
PageRank | References | Authors |
21.75 | 3 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Richard M. Wilson | 1 | 697 | 340.86 |