dc.contributor.author Siegel, Angela Annette dc.date.accessioned 2011-05-02T12:10:13Z dc.date.available 2011-05-02T12:10:13Z dc.date.issued 2011-05-02 dc.identifier.uri http://hdl.handle.net/10222/13499 dc.description.abstract This thesis explores the structure of games, including both the internal structure of various games and also the structure of classes of games as partially ordered sets. Internal structure is explored through consideration of juxtapositions of game positions and how the underlying games interact. We look at ordinal sums and introduce side-sums as a means of understanding this interaction, giving a full solution to a Toppling Dominoes variant through its application. Loopy games in which only one player is allowed a pass move, referred to as Oslo games, are introduced and their game structure explored. The poset of Oslo games is shown to form a distributive lattice. The Oslo forms of Wythoff’s game, Grundy’s game and octal .007 are introduced and full solutions given. Finally, the poset of option-closed games is given up to day 3 and all are shown to form a planar lattice. The option-closed game of Cricket Pitch is also fully analyzed. en_US dc.language.iso en en_US dc.subject combinatorial game theory en_US dc.subject option-closed en_US dc.subject lattice en_US dc.subject Oslo games en_US dc.subject side-sum en_US dc.subject ordinal sum en_US dc.subject juxtaposition en_US dc.subject Cricket Pitch en_US dc.subject Toppling Dominoes en_US dc.subject loopy games en_US dc.subject Oslo Grundy's Game en_US dc.subject Oslo Wythoff's Game en_US dc.subject octal .007 en_US dc.title ON THE STRUCTURE OF GAMES AND THEIR POSETS en_US dc.type Thesis en_US dc.date.defence 2011-04-21 dc.contributor.department Department of Mathematics & Statistics - Math Division en_US dc.contributor.degree Doctor of Philosophy en_US dc.contributor.external-examiner Dr. Daniel Ullman en_US dc.contributor.graduate-coordinator Dr. Sara Faridi en_US dc.contributor.thesis-reader Dr. Jason I. Brown en_US dc.contributor.thesis-reader Dr. David Wolfe en_US dc.contributor.thesis-supervisor Dr. Richard J. Nowakowski en_US dc.contributor.ethics-approval Not Applicable en_US dc.contributor.manuscripts Not Applicable en_US dc.contributor.copyright-release Not Applicable en_US
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