Turan, Paul

Turán's problem for hypergraphs ★★

Author(s): Turan

Conjecture Every simple $3$ -uniform hypergraph on $3n$ vertices which contains no complete $3$ -uniform hypergraph on four vertices has at most $\frac12 n^2(5n-3)$ hyperedges.

Conjecture Every simple $3$ -uniform hypergraph on $2n$ vertices which contains no complete $3$ -uniform hypergraph on five vertices has at most $n^2(n-1)$ hyperedges.

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Posted by fhavet
updated March 12th, 2013

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Number Theory » Additive N.T.

The Erdos-Turan conjecture on additive bases ★★★★

Author(s): Erdos; Turan

Let $B \subseteq {\mathbb N}$ . The representation function $r_B : {\mathbb N} \rightarrow {\mathbb N}$ for $B$ is given by the rule $r_B(k) = \#\{ (i,j) \in B \times B : i + j = k \}$ . We call $B$ an additive basis if $r_B$ is never $0$ .