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{\bf R.H. Jeurissen}
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{\bf Sets in the Plane with Many Concyclic Subsets}
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We study sets of points in the Euclidean plane having property $R(t,s)$:
every $t$-tuple of its points contains a concyclic $s$-tuple.
Typical examples of the kind of theorems we prove are:
a set with $R(19,10)$ must have all its points on two circles or
all its points, with the exception of at most 9, are on one circle;
of a set with $R(8,5)$ and $N\geq 28$ points at least $N-3$ points
lie on one circle; a set of at least 109 points with $R(7,4)$ has
$R(109,7)$. We added some results on the analogous configurations
in 3-space.

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