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| Content Provider | ACM Digital Library |
|---|---|
| Author | Lovett, Shachar Kuperberg, Greg Peled, Ron |
| Abstract | We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise permutations. In all cases, the sizes of the objects are optimal up to polynomial overhead. The proof of existence is probabilistic. We show that a randomly chosen such object has the required properties with positive yet tiny probability. The main technical ingredient is a special local central limit theorem for suitable lattice random walks with finitely many steps. |
| Starting Page | 1091 |
| Ending Page | 1106 |
| Page Count | 16 |
| File Format | PDF MP4 |
| ISBN | 9781450312455 |
| DOI | 10.1145/2213977.2214075 |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 2012-05-19 |
| Publisher Place | New York |
| Access Restriction | Subscribed |
| Subject Keyword | Permutations Designs Local central limit theorem Probabilistic method Orthogonal arrays |
| Content Type | Audio Text |
| Resource Type | Article |
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