Counting Lattice Triangulations
| dc.creator | Kaibel, Volker | |
| dc.creator | Ziegler, Günter M. | |
| dc.date | 2002-11-18 | |
| dc.date | 2002-12-13 | |
| dc.date.accessioned | 2026-07-07T04:53:02Z | |
| dc.date.available | 2026-07-07T04:53:02Z | |
| dc.description | 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 $m\times n$. 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 flips. | |
| dc.description | 30 pages, to appear in: ``British Combinatorial Surveys'' (C. D. Wensley, ed.), Cambridge University Press, 2003. This is an updated version containing minor changes suggested by the referee | |
| dc.identifier | https://arxiv.org/abs/math/0211268 | |
| dc.identifier | http://arxiv.org/abs/math/0211268 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65691 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 05AXX; 52B20 | |
| dc.title | Counting Lattice Triangulations | |
| dc.type | text |