Table of Contents

Combinatorics

Summer 2025
Stefan Felsner

Content of individual lectures: 1 , 2 , 3 , 4 ,

1. lecture, 15.04.2025 

   What is Combinatorics - introductory examples
     Derangements
       Aspects of counting derangements (fixed point free permutations) P.R.de Montmort
       sequence A000166 in OEIS
       recurrence - summation
2. lecture, 17.04.2025 
                    - asymptotics - generating function
     Orthogonal Latin Squares 
       (Euler's 36 officers problem)
       Orthogonal Latin squares of odd order from groups
       MOLS (mutually orthogonal Latin squares)
       There are at most n-1 MOLS of order n
       Projective planes
3. lecture, 22.04.2025 
   Basic Counting
     Basic rules for counting
     Binomial coefficients
        Models and identities
        Extending binomial coefficients
4. lecture, 24.04.2025 
        Extending binomial identities to polynomial identities
        The binomial theorem
    Combinatorics of Permutations
        The type of a permutation
        Enumeration of permutations of given type
        Permutations with k cycles

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