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National Repository of Grey Literature

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Exponential function and Mayer expansion Nagy, Oliver ; Zahradník, Miloš (advisor) ; Loebl, Martin (referee) Title: Exponential function and Mayer expansion Author: Oliver Nagy Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Miloš Zahradník, CSc., Department of Mathematical Analysis Abstract: The unifying topic of this thesis is cluster expansion in statistical phy- sics. It is divided into three chapters. In the first one we present the necessary mathematical apparatus - selected topics from combinatorics, graph theory and theory of generating functions. The second one is an introduction to cluster expan- sion and abstract polymer model. Finally, in the third chapter we show a new resummation method for partition function of hard-core repulsive abstract poly- mer model. In this resummation we make use of cancellations of terms in partition function to rewrite the sum of clusters to a sum of quilted clusters, or alternati- vely as a sum of "bunches". The methods we use in this final chapter are original and may lead to some new results. Keywords: binomial and multinomial formula; power series; inclusion-exclusion principle; cluster expansion. iii Detailed record

Combinatorial principles in school mathematics BŘEZINOVÁ, Jiřina The thesis includes delatiled explanation of combinatorial principles used in school mathematics. The single principles are explained in details and practicised. The tasks at the end of the chapter serve readers for testing acquired knoledge. Detailed record

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