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The course will focus on solving combinatorial problems by application of
generating functions, with emphasis on methods based on complex analysis. No
previous knowledge of complex analysis is necessary, but basic knowledge of
generating functions is expected.
Last update: IUUK (16.05.2012)
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Oral exam with time for written prepapration. Last update: Jelínek Vít, doc. RNDr., Ph.D. (10.06.2019)
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Herbert S. Wilf: Generatingfunctionology. Academic Press, 1993. ISBN 0-12-751956-4
Philippe Flajolet, Robert Sedgewick: Analytic Combinatorics. Cambridge University Press, 2009. ISBN 978-0-521-89806-5 Last update: IUUK (16.05.2012)
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The exam is oral, with the possibility of a written preparation. The exam covers the material presented at the lectures, including the ability to apply the theory presented at the lectures to solve specific combinatorial exercises. Last update: Jelínek Vít, doc. RNDr., Ph.D. (25.02.2019)
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Formal power series. Lagrange inversion formula. Ordinary and exponential generating functions, and the combinatorial interpretation of their basic operations. Overview of basic theory of complex analytic functions. Rational and meromorphic functions, the residue theorem. Applications of complex analysis to the enumeration of combinatorial objects. Multivariate generating functions, and their application to the study of random combinatorial objects. Last update: IUUK (16.05.2012)
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