Lattice point methods for combinatorial games
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 thesisDepartment
MathematicsPermalink
https://hdl.handle.net/10161/3749Citation
Guo, Alan (2011). Lattice point methods for combinatorial games. Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/3749.Collections
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