51 lessons in Combinatorics

Basic countingCount the oppositeCaseworkPermutations & combinationsPermutations with repetitionRestrictions: glue and the fussy one firstGaps: no two togetherStars and barsGrid pathsReading $\lfloor x \rfloor$ and $\lceil x \rceil$Inclusion-exclusionRecursion: split by the last moveThe pigeonhole principleProbability by countingTree diagramsSymmetry and simple bijectionsBinomial theoremGenerating functions introCatalan numbersDerangementsStirling & Bell numbersInteger partitionsRamsey theory introBurnside's lemma & Pólya enumerationYoung tableauxDesign theory & Latin squaresError-correcting codes (intro)Proof of inclusion-exclusionProof: Catalan number formulaBijective proofsCombinatorial game theory (Nim)Probabilistic methodExponential generating functionsThe twelvefold wayLattice paths & the ballot problemPartition generating functions & Euler's pentagonal theoremSperner's & Dilworth's theoremsGaussian binomial coefficientsThe hook length formulaSteiner systems & Fisher's inequalityPosets, lattices & Möbius functionsAnalytic combinatorics & the symbolic methodThe transfer matrix methodExtremal set theoryMatroid theoryThe Combinatorial NullstellensatzThe Lovász local lemmaAdditive combinatorics & sumsetsPermutation patterns & avoidanceDescents & Eulerian numbersThe permanent

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