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Dana Randall, Günter Rote, Francisco Santos, and Jack Snoeyink:

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Counting triangulations and pseudo-triangulations of wheels

*In: Proceedings of the 13th Canadian Conference on Computational Geometry,
Waterloo, August 6-10, 2001. Editor: T. Biedl; pp. 149-152.*
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Abstract

Motivated by several open questions on triangulations and pseudotriangulations,we
give closed form expressions for the number of triangulations and the number
of minimum pseudo-triangulations of *n* points in wheel configurations,
that is, with *n*-1 in convex position.Although the numbers of triangulations
and pseudotriangulations vary depending on the placement of the interior
point, their difference is always the (*n*-2)^{nd} Catalan
number.

We also prove an inequality #PT <= 3^{i}#T for the
numbers of minimum pseudo-triangulations and triangulations of any point
configuration with *i* interior points.
Last update: March 12, 2002.