Geodesic
The polytope of all triangulations of a point configuration
Documenta mathematica, Tome 1 (1996), pp. 113-119.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the convex hull $P_{\cal A}$ of the 0-1 incidence vectors of all triangulations of a point configuration ${\cal A}$. This was called the universal polytope in citeBIFIST. The affine span of $P_{\cal A}$ is described in terms of the co-circuits of the oriented matroid of ${\cal A}$. Its intersection with the positive orthant is a quasi-integral polytope $Q_{\cal A}$ whose integral hull equals $P_{\cal A}$. We present the smallest example where $Q_{\cal A}$ and $P_{\cal A}$ differ. The duality theory for regular triangulations in citeBIGEST is extended to cover all triangulations. We discuss potential applications to enumeration and optimization problems regarding all triangulations.
Classification : 52B55, 90C27 
@article{DOCMA_1996__1__a16,
     author = {De Loera, Jes\'us A. and Hosten, Serkan and Santos, Francisco and Sturmfels, Bernd},
     title = {The polytope of all triangulations of a point configuration},
     journal = {Documenta mathematica},
     pages = {113--119},
     publisher = {mathdoc},
     volume = {1},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1996__1__a16/}
}
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De Loera, Jesús A.; Hosten, Serkan; Santos, Francisco; Sturmfels, Bernd. The polytope of all triangulations of a point configuration. Documenta mathematica, Tome 1 (1996), pp. 113-119. http://geodesic.mathdoc.fr/item/DOCMA_1996__1__a16/