Tropical convexity via cellular resolutions
Florian Block1
and Josephine Yu2
1Technische Universität München, Zentrum Mathematik Boltzmannstr. 3 85748 Garching Germany Boltzmannstr. 3 85748 Garching Germany
2University of California Department of Mathematics Berkeley CA 94720 Berkeley CA 94720
2University of California Department of Mathematics Berkeley CA 94720 Berkeley CA 94720
DOI: 10.1007/s10801-006-9104-9
Abstract
The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls. Tropical cyclic polytopes are also presented.
Pages: 103–114
Full Text: PDF
References
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2. M. Develin and B. Sturmfels, “Tropical Convexity”, Documenta Math. 9 (2004): 1-27.
3. D. R. Grayson and M. E. Stillman, Macaulay 2, a software system for research in algebraic geometry,
2002. Available at http://www.math.uiuc.edu/Macaulay2/.
4. M. Joswig, “Tropical Halfspaces”, arXiv: math.CO/0312068, 2003.
5. Maple. Available at http://maplesoft.com.
6. E. Miller and B. Sturmfels, Combinatorial Commutative Algebra, Graduate Texts in Mathematics, Springer, 2004.
7. R. A. Milowski, Computing Irredundant Irreducible Decompositions of Large Scale Monomial Ideals, ISSAC 2004, Santanders, Spain,
2004. Software available at http://milowski. org/software.html.
8. K. Polthier, JavaView, a 3D geometry viewer and a mathematical visualization software. Available at