Algebras, Synchronous Games and Chromatic Numbers of Graphs

We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game, this leads to characterizations in terms of properties of a...

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Bibliographic Details
Published inarXiv.org
Main Authors Helton, William, Meyer, Kyle P, Paulsen, Vern I, Satriano, Matthew
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.03.2017
Subjects
Algebra
Game theory
Graph coloring
Graphical representations
Rings (mathematics)
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Summary:We associate to each synchronous game an algebra whose representations determine if the game has a perfect deterministic strategy, perfect quantum strategy or one of several other perfect strategies. when applied to the graph coloring game, this leads to characterizations in terms of properties of an algebra of various quantum chromatic numbers that have been studied in the literature. This allows us to develop a correspondence between various chromatic numbers of a graph and ideals in this algebra which can then be approached via various Grobner basis methods.
ISSN:2331-8422