[see also: estimate]
The above bound on $a_n$ is close to best possible $\langle$to the best possible$\rangle$.
We conclude that, no matter what the class of $b$ is, we have an upper bound on $M$.
The main new feature is the use of the face ring to produce lower bounds for the number of vertices.
Kim announces that (by a tedious proof) the upper bound can be reduced to 10.
[see also: dominate, estimate]
$F$ is bounded above $\langle$below$\rangle$ by a constant times $f(z)$.
Then $G$ is bounded away from zero.
Furthermore, $K$ is an upper bound on $\langle$for$\rangle$ $f(x)$ for $x$ in $K$.
Theorem 1 can be used to bound the number of such $T$.
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