On the Number of Pseudo-Triangulations of Certain Point Sets

Details On the Number of Pseudo-Triangulations of Certain Point Sets On the Number of Pseudo-Triangulations of Certain Point Sets

2006-01-31

arxiv.org/abs/math/0601747v2

J. Combin. Theory Ser. A, 115 (2008) 254-278.

Mathematics

Combinatorics

31 pages, 11 figures, 4 tables. Not much technical changes with respect to v1, except some proofs and statements are slightly

Scientific paper

10.1016/j.jcta.2007.06.002

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically $12^n n^{\Theta(1)}$ pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far.

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