On Subsets with Cardinalities of Intersections Divisible by a Fixed Integer

P. Frankl, A. M. Odlyzko

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

If m(n, l) denotes the maximum number of subsets of an n-element set such that the intersection of any two of them has cardinality divisible by l, then a trivial construction shows that m(n,l)≥2 [n/l] For l= 2, this was known to be essentially best possible. For l ⩾ 3, we show by construction that m(n, l)2−[n/l] grows exponentially in n, and we provide upper bounds.

Original languageEnglish (US)
Pages (from-to)215-220
Number of pages6
JournalEuropean Journal of Combinatorics
Volume4
Issue number3
DOIs
StatePublished - Jan 1 1983

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