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Set Systems with Restricted Intersections modulo Prime Powers

✍ Scribed by László Babai; Péter Frankl; Samuel Kutin; Daniel Štefankovič

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
236 KB
Volume
95
Category
Article
ISSN
0097-3165

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✦ Synopsis

We study set systems satisfying Frankl Wilson-type conditions modulo prime powers. We prove that the size of such set systems is polynomially bounded, in contrast with V. Grolmusz's recent result that for non-prime-power moduli, no polynomial bound exists. More precisely we prove the following result.

Theorem. Let p be a prime and q= p k . Let + 1 , ..., + s be distinct integers, 0 + i q&1. Let X be a set of n elements and let A 1 , A 2 , ..., A m be subsets of X with the following properties:

v For all i, j (1 i< j m), there exists l (1 l s) such that

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