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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Restricted Universes of Partizan Misere Games

Milley, Rebecca 25 March 2013 (has links)
This thesis considers three restricted universes of partizan combinatorial games and finds new results for misere play using the recently-introduced theory of indistinguishability quotients. The universes are defined by imposing three different conditions on game play: alternating, dicot (all-small), and dead-ending. General results are proved for each main universe, which in turn facilitate detailed analysis of specific subuniverses. In this way, misere monoids are constructed for alternating ends, for pairs of day-2 dicots, and for normal-play numbers, as well as for sets of positions that occur in variations of nim, hackenbush, and kayles, which fall into the alternating, dicot, and dead-ending universes, respectively. Special attention is given to equivalency to zero in misere play. With a new sufficiency condition for the invertibility of games in a restricted universe, the thesis succeeds in demonstrating the invertibility (modulo specific universes) of all alternating ends, all but previous-win alternating non-ends, all but one day-2 dicot, over one thousand day-3 dicots, hackenbush ‘sprigs’, dead ends, normal-play numbers, and partizan kayles positions. Connections are drawn between the three universes, including the recurrence of monoids isomorphic to the group of integers under addition, and the similarities of universe-specific outcome determinants. Among the suggestions for future research is the further investigation of a natural and promising subset of dead-ending games called placement games.
2

Jeux combinatoires dans les graphes / Combinatorial games on graphs

Renault, Gabriel 29 November 2013 (has links)
Dans cette thèse, nous étudions les jeux combinatoires sousdifférentes contraintes. Un jeu combinatoire est un jeu à deux joueurs, sanshasard, avec information complète et fini acyclique. D’abord, nous regardonsles jeux impartiaux en version normale, en particulier les jeux VertexNimet Timber. Puis nous considérons les jeux partisans en version normale, oùnous prouvons des résultats sur les jeux Timbush, Toppling Dominoeset Col. Ensuite, nous examinons ces jeux en version misère, et étudionsles jeux misères modulo l’univers des jeux dicots et modulo l’univers desjeux dead-endings. Enfin, nous parlons du jeu de domination qui, s’il n’estpas combinatoire, peut être étudié en utilisant des outils de théorie des jeuxcombinatoires. / In this thesis, we study combinatorial games under differentconventions. A combinatorial game is a finite acyclic two-player game withcomplete information and no chance. First, we look at impartial gamesin normal play and in particular at the games VertexNim and Timber.Then, we consider partizan games in normal play, with results on the gamesTimbush, Toppling Dominoes and Col. Next, we look at all these gamesin misère play, and study misère games modulo the dicot universe and modulothe dead-ending universe. Finally, we talk about the domination game which,despite not being a combinatorial game, may be studied with combinatorialgames theory tools.

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