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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* (CCCG'01), Waterloo, August 6–10, 2001. Editor:
T. Biedl; pp. 149–152.
→BibTeX
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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.