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Lattice point methods for combinatorial games

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Date
2011
Author
Guo, Alan
Advisor
Miller, Ezra
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Abstract
We encode arbitrary finite impartial combinatorial games in terms oflattice points in rational convex polyhedra. Encodings provided by theselatticegamescan be made particularly efficient for octal games, which we generalize tosquarefree games. These encompass all heap games in a natural setting where theSprague–Grundy theorem for normal play manifests itself geometrically. We providepolynomial time algorithms for computing strategies for lattice games provided thatthey have a certain algebraic structure, called anaffine stratification.
Type
Honors thesis
Department
Mathematics
Permalink
https://hdl.handle.net/10161/3749
Citation
Guo, Alan (2011). Lattice point methods for combinatorial games. Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/3749.
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This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.

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