{"id":{"repo_id":"ucf","oai_identifier":"oai:stars.library.ucf.edu:etd-1121"},"canonical_url":"https://search.dev.ndltd.org/etd/ucf/oai:stars.library.ucf.edu:etd-1121","repository":{"repo_id":"ucf","name":"Central Florida","base_url":"https://stars.library.ucf.edu/do/oai/"},"display":{"title":"Macmahon's Master Theorem And Infinite Dimensional Matrix Inversion","abstract":"MacMahon's Master Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. We give a complete proof of MacMahon's Master Theorem based on MacMahon's original 1960 proof. We also study a specific infinite dimensional matrix inverse due to C. Krattenthaler.","abstract_html":"MacMahon&#x27;s Master Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. 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