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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
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