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GEOMETRICAL REALIZATION OF SET SYSTEMS AND PROBABILISTIC C01vf1v1UNICATION COMPLEXITY
 

Summary: GEOMETRICAL REALIZATION OF SET SYSTEMS AND
PROBABILISTIC C01vf1v1UNICATION COMPLEXITY
N. Alon* - P. Frankl** - V. Rodl**
*Department of Mathematics, Tel Aviv University, Tel Aviv and
Bell Communications Research, Morristown, New Jersey 07960 USA
**AT&T Bell Labs, Murray Hill, New Jersey, 07974 USA
Theorem 1 1.
ABSTRACT
In this paper we prove:
If n,m -+-00 and log2m = o(n) then d(n,m)s(t + o(l))n (i)
Corollary 1 2.
1
n/32 S d(n, n) S (2 + 0(1)) . n
(The constant 1/32 can be somewhat improved).
Qoro)]ary 1 3.
If m /n 2 -+ 00 and (log2m )In -+- 0 then,
Put d = d( n, m) , then for every integer 1 S h S nm (iii)
(8 rn;: kn+mJd+h+m ~ 2nm
We specify two special cases separately.
d(n, m) = (t + 0(1)) . n .

  

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

 

Collections: Mathematics