Suites Maximales Dans Les Carquois Cycliques À Trois Points
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Les algèbres amassées sont des classes d'algèbres introduites dans les années 2000 par Sergey Fomin et Andrei Zelevinsky, dans leurs recherches sur les bases canoniques duales et la positivité totale dans les groupes semi-simples. Populaires dès leur découverte, elles ont été étudiées par d'autres scientifiques comme nouvelle approche dans leurs champs de recherche. Elles sont maintenant utilisées dans plusieurs domaines des mathématiques, ainsi qu'en physique. Par contre, un des hics de cette théorie est que les variables amassés peuvent devenir difficiles à calculer très rapidement. C'est là que les carquois et les suites de mutations vertes entrent en jeu. Ces deux éléments permettent d'avoir une approche combinatoire et plus visuelle des algèbres amassées, de sorte que le travail est simplifié et plus facile d'approche. Ce travail se concentre sur l'étude des suites maximales de mutations vertes dans les carquois cycliques à trois points. Plus précisément, le but est de trouver des exemples de carquois qui n'en ont aucune. Nous étudierons plus en détail un exemple trouvé par Brüstle, Dupont et Pérontin, puis nous trouverons un moyen de le généraliser.
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