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.
Author: | Volker Kaibel, Günter M. Ziegler |
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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 |