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Counting Lattice Triangulations

Please always quote using this URN:urn:nbn:de:0296-matheon-116
  • We discuss the problem to count, or, more modestly, to estimate the number f(m; n) of unimodular triangulations of the planar grid of size m * n. Among other tools, we employ recursions that allow one to compute the (huge) number of triangulations for small m and rather large n by dynamic programming; we show that this computation can be done in polynomial time if m is fixed, and present computational results from our implementation of this approach. We also present new upper and lower bounds for large m and n, and we report about results obtained from a computer simulation of the random walk that is generated by ips.

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Metadaten
Author:Volker Kaibel, Günter M. Ziegler
URN:urn:nbn:de:0296-matheon-116
Referee:Rolf H. Möhring
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2003/12/15
Release Date:2003/12/15
Preprint Number:9
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