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Set systems with no union of cardinality 0 modulo N. Alon, IBM Almaden and Tel Aviv University
 

Summary: Set systems with no union of cardinality 0 modulo
m
N. Alon, IBM Almaden and Tel Aviv University
D. Kleitman, MIT
R. Lipton, Princeton University
R. Meshulam, MIT
M. Rabin, Hebrew University and Harvard University
J. Spencer, Courant Institute
Abstract
Let q be a prime power. It is shown that for any hypergraph
F = {F1, . . . , Fd(q-1)+1} whose maximal degree is d, there exists =
F0 F, such that | F F0
F| 0 (mod q).
For integers d, m 1 let fd(m) denote the minimal t such that for
any hypergraph F = {F1, . . . , Ft} whose maximal degree is d, there
exists = F0 F, such that | F F0
F| 0 (mod m).
Here we determine fd(m) when m is a prime power, and remark on
the general case.
Example: Let Aij 1 i m - 1, 1 j d , be pairwise disjoint

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics