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Course, academic year 2022/2023
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Combinatorial Counting - NDMI015
Title: Kombinatorické počítání
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://kam.mff.cuni.cz/~klazar/KPOC19.html
Guarantor: doc. RNDr. Martin Klazar, Dr.
Class: Informatika Mgr. - Diskrétní modely a algoritmy
Classification: Informatics > Discrete Mathematics
Annotation -
Last update: T_KAM (07.05.2001)
Introduction to enumerative combinatorics. Basic techniques (ordinary and exponential generating functions, Lagrange inversion formula, bijective proofs) are explained on a number of concrete examples in which we shall count combinatorial structures of various kinds.
Aim of the course -
Last update: T_KAM (20.04.2008)

Students learn the fundamental technique of combinatorial enumeration, which are generating functions.

Course completion requirements -
Last update: doc. RNDr. Martin Klazar, Dr. (14.05.2020)

Oral exam, with written preparation. Exam question are/will be given on the course page,

see teacher's web page.

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As to situation caused by the current coronavirus pandemia in spring and summer 2020.

Form of exam (contact or distant) will be determined for each term in SIS

according to actual situation. Contact exam will be writen one with possible oral part.

For this course the contact form in small groups (<6, <11 people) appears probable.

Literature -
Last update: T_KAM (20.04.2008)

R.P. Stanley: Enumerative combinatorics I, Wandswort & Brooks, 1986.

R.P. Stanley: Enumerative combinatorics II, Cambridge University Press, 1999.

Requirements to the exam -
Last update: doc. RNDr. Martin Klazar, Dr. (14.05.2020)

Oral exam, with written preparation. Exam question are/will be given on the course page,

see teacher's web page.

************************************************************************

As to situation caused by the current coronavirus pandemia in spring and summer 2020.

Form of exam (contact or distant) will be determined for each term in SIS

according to actual situation. Contact exam will be writen one with possible oral part.

For this course the contact form in small groups (<6, <11 people) appears probable.

Syllabus -
Last update: T_KAM (20.04.2008)

1. Problems of combinatorial enumeration. 2. Bijections. 3. Generating functions. 4. Exponential and composition formula. 5. Lagrange's inversion formula. 6. Asymptotic estimates.

 
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