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Course, academic year 2023/2024
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Combinatorial Structures - NDMI036
Title: Kombinatorické struktury
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Jan Kratochvíl, CSc.
Class: Informatika Mgr. - Diskrétní modely a algoritmy
Classification: Informatics > Discrete Mathematics
Annotation -
Last update: T_KAM (06.05.2001)
Advanced course in Computer Science Survey of regular structures, constructions and existence-nonexistence theorems (finite planes and geometries, block designs, Steiner triple systems, mutually orthogonal Latin squares, difference sets, Hadamard matrices).
Course completion requirements -
Last update: prof. RNDr. Jan Kratochvíl, CSc. (23.09.2020)

Oral exam. The exam may be performed remotely.

Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

Hall, M. Jr.: Combinatorial Theory, Wiley, New York, 1986

Requirements to the exam -
Last update: prof. RNDr. Jan Kratochvíl, CSc. (23.09.2020)

The exam is oral and may be performed remotely. The knowledge and skills examined correspond to the syllabus in extent presented during the lectures. Common understanding to all notions and their relationship, theorems including proofs and ability to apply the acquired skills to simple situations related to the topics of the class are subject of the examination.

Syllabus -
Last update: prof. Mgr. Milan Hladík, Ph.D. (01.04.2015)

Basic combinatorial structures.

1. Finite geometries.

2. Finite projective planes.

3. Balanced incomplete block designs.

4. Steiner triple systems.

5. Symmetric designs, Bruck-Ryser-Chowla theorem.

6. Hadamard matrices.

7. Mutually ortogonal Latin squares.

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