TY - JOUR
T1 - On Subsets with Cardinalities of Intersections Divisible by a Fixed Integer
AU - Frankl, P.
AU - Odlyzko, A. M.
PY - 1983
Y1 - 1983
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84911563493&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84911563493&partnerID=8YFLogxK
U2 - 10.1016/S0195-6698(83)80014-6
DO - 10.1016/S0195-6698(83)80014-6
M3 - Article
AN - SCOPUS:84911563493
SN - 0195-6698
VL - 4
SP - 215
EP - 220
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 3
ER -