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Abzhltheorie nach Plya
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Im Zentrum dieses essentials steht der gefeierte Abzhlsatz von Plya. Damit lassen sich kombinatorische Objekte mit Symmetrien abzhlen, wie etwa Halsketten mit bunten Perlen und Wrfel mit gefrbten Seiten, aber auch Graphen und Bume. Die Gruppentheorie wird dafr benutzt, die Symmetrien der abzuzhlenden Figuren zu beschreiben. Darauf aufbauend kann anhand der Operation der jeweiligen Symmetriegruppe auf den gefrbten Figuren die Anzahl der verschiedenen Muster ermittelt werden. Grundlegend hierfr ist das Lemma von Burnside. Aus seiner gewichteten Fassung wird unter Einbeziehung der Zyklenindexpolynome von Symmetriegruppen der berhmte Plyasche Satz hergeleitet. Einige Beispiele runden die Darstellung ab.
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