Probabilistic existence of rigid combinatorial structures

Greg Kuperberg, Shachar Lovett, Ron Peled

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationSTOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
Pages1091-1105
Number of pages15
DOIs
StatePublished - 2012
Event44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, United States
Duration: 19 May 201222 May 2012

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing

Conference

Conference44th Annual ACM Symposium on Theory of Computing, STOC '12
Country/TerritoryUnited States
CityNew York, NY
Period19/05/1222/05/12

Keywords

  • designs
  • local central limit theorem
  • orthogonal arrays
  • permutations
  • probabilistic method

All Science Journal Classification (ASJC) codes

  • Software

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