TY - GEN

T1 - Probabilistic existence of rigid combinatorial structures

AU - Kuperberg, Greg

AU - Lovett, Shachar

AU - Peled, Ron

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - designs

KW - local central limit theorem

KW - orthogonal arrays

KW - permutations

KW - probabilistic method

UR - http://www.scopus.com/inward/record.url?scp=84862632182&partnerID=8YFLogxK

U2 - 10.1145/2213977.2214075

DO - 10.1145/2213977.2214075

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84862632182

SN - 9781450312455

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1091

EP - 1105

BT - STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing

T2 - 44th Annual ACM Symposium on Theory of Computing, STOC '12

Y2 - 19 May 2012 through 22 May 2012

ER -