- Basic understanding to count functions with finite input and output sets (the twelve-fold way) [K2, K4];
- Finding bijections and enumerating combinatorial objects (at random) by rank functions [K2,K4];
- Dealing with partitions and understanding the basic theory of partitions [K2,K4];
- Applying group actions to model objects with symmetries [K2,K3];
- Application of the Cauchy-Frobenius Lemma (Burnside Lemma) to non-trivial counting problems [K2,K4];
- Applying Polya theory with refined and improved versions of the Cauchy-Frobenius Lemma [K3,K4,K5].
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Stirling numers of fist and second kind, partition function, Omega-operator, subgroups of the symmetric group, group action, Cauchy-Frobenius Lemma, Polya's theorem, cycle index polynomial.
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