Inside-out polytopes
By Matthias Beck, Thomas Zaslavsky. 2003
92 citations recorded by the source corpus.
We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an integer whose parts are partially distinct, and generalized latin squares. Our method is to generalize Ehrhart's theory of lattice-point counting to a convex polytope dissected by a hyperplane arrangement. We particularly develop the applications to graph and signed-graph coloring, compositions of an integer, and antimagic labellings.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Signal Processing
View Paper: https://www.semanticscholar.org/paper/ec81f81307bb3c47dc91875a7138765dbca620f3
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In Artificial Intelligence
In Discrete Mathematics and Combinatorics
- Lindsay C. Piechnik
- Francisco Santos
- Christian Haase
- Andreas Paffenholz
- M. Develin
- Alexander Postnikov
- Federico Ardila
- Bernd Sturmfels
In Signal Processing
Citations in the corpus
- Existence of unimodular triangulations — positive results (2014, methodology): “ulations exist they have the same f-vector. For example, the chromatic polynomial of a graph can be interpreted as the Ehrhart polynomial of the complement of a hyperplane arrangement in the 0/1-cube [16]. This hyperplane arrangement is compatible with the standard unimodular triangulation of the cu”