SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Analytic combinatorics - NDMI087
Title in English: Analytická kombinatorika
Guaranteed by: Computer Science Institute of Charles University (32-IUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:2/1 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Vít Jelínek, Ph.D.
Class: Informatika Mgr. - volitelný
Classification: Informatics > Discrete Mathematics
Annotation -
Last update: (16.05.2012)
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.
Course completion requirements - Czech
Last update: doc. RNDr. Vít Jelínek, Ph.D. (10.06.2019)

Ústní zkouška s možností písemné přípravy.

Literature -
Last update: (16.05.2012)

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

Requirements to the exam -
Last update: doc. RNDr. Vít Jelínek, Ph.D. (25.02.2019)

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.

Syllabus -
Last update: (16.05.2012)

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.

 
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