Lattice point methods for combinatorial games

dc.contributor.advisor

Miller, Ezra

dc.contributor.author

Guo, Alan

dc.date.accessioned

2011-05-12T01:09:41Z

dc.date.issued

2011

dc.department

Mathematics

dc.description.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.

dc.identifier.uri

https://hdl.handle.net/10161/3749

dc.language.iso

en_US

dc.title

Lattice point methods for combinatorial games

dc.type

Honors thesis

pubs.organisational-group

Duke

pubs.organisational-group

Duke

pubs.organisational-group

Trinity College of Arts & Sciences

pubs.organisational-group

Duke

pubs.organisational-group

Trinity College of Arts & Sciences

pubs.organisational-group

Mathematics

pubs.organisational-group

Duke

pubs.organisational-group

Trinity College of Arts & Sciences

pubs.organisational-group

Statistical Science

pubs.publication-status

Published

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
guo_seniorthesis_final.pdf
Size:
367.17 KB
Format:
Adobe Portable Document Format