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Lecturer(s)
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Švrček Jaroslav, RNDr. CSc.
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Lachman Dominik, Mgr.
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Course content
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1. Special properties of permutations, graphs and degrees of permutations, applications. 2. The reccurence method in combinatorics, solving linear reccurence. 3. Generating functions. 4. Introduction to the combinatorial geometry. Polyominoes. 5. Combinatorics of convex polygons, the Cayley theorem. 6. Reccursive methods in combinatorial geometry.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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1. Special properties of permutations, graphs and degrees of permutations, applications. 2. The reccurence method in combinatorics, solving linear reccurence. 3. Generating functions. 4. Introduction to the combinatorial geometry. Polyominoes. 5. Combinatorics of convex polygons, the Cayley theorem. 6. Reccursive methods in combinatorial geometry.
3. Aplication Apply knowledges of basic combinatorial methods and principles.
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Prerequisites
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unspecified
KAG/MUKO3
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Assessment methods and criteria
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Oral exam, Seminar Work
Credit: the student has to solve 10 combinatorial problems (homework) assigned during the course and has to pass one written test (i.e. to obtain at least half of the possible points). Exam: the student has to understand the subject and be able to prove the principal results.
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Recommended literature
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Golomb S. W. (1994). Polyminoes (Puzzles, Patterns, Problems and Packing). Princetown University Press New Jersey.
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HADWIGER H., Debrunner H. (1966). Combinatorial Geometry in the Plane. Nauka Moskva.
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Herman J., Kučera R., Šimša J. (1997). Metody řešení matematických úloh II. MU Brno.
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Markus A. (1988). Combinatorics (a Problem Oriented Approach). MAA Washington.
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Švrček J. (2003). Úvod do kombinatoriky. VUP OLomouc.
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