18.212 | Spring 2019 | Undergraduate

Algebraic Combinatorics

Lecture Notes

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18.212 S19 Algebraic Combinatorics, Lecture 1: Catalan numbers I
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18.212 S19 Algebraic Combinatorics, Lecture 1: Catalan numbers II
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18.212 S19 Algebraic Combinatorics, Lecture 10: Statistics on permutations and more
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18.212 S19 Algebraic Combinatorics, Lecture 11: Stirling numbers and more
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18.212 S19 Algebraic Combinatorics, Lecture 12: Eulerian numbers. Increasing binary trees. 3 Pascal-like triangles
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18.212 S19 Algebraic Combinatorics, Lecture 13: Discussion of Problem Set 1
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18.212 S19 Algebraic Combinatorics, Lecture 14: Discussion of Problem Set 1 (cont.)
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18.212 S19 Algebraic Combinatorics, Lecture 15: Posets and lattices. Boolean lattice. Partition lattice. Young's lattice
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18.212 S19 Algebraic Combinatorics, Lecture 16: Distributive lattices. Birkhoff's fundamental theorem for finite distributive lattices
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18.212 S19 Algebraic Combinatorics, Lecture 17: Sperner's property and more
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18.212 S19 Algebraic Combinatorics, Lecture 18: Greene's theorem vs Schensted correspondence and more
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18.212 S19 Algebraic Combinatorics, Lecture 19: Differential posets and more
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18.212 S19 Algebraic Combinatorics, Lecture 20: Proof of unimodality of Gaussian coefficients and more
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18.212 S19 Algebraic Combinatorics, Lecture 21: Partition theory (cont.). Franklin's combinatorial proof of Euler's pentagonal number theorem and more
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18.212 S19 Algebraic Combinatorics, Lecture 22: Partition theory (cont.). Combinatorial proof of Jacobi's triple product identity and more
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18.212 S19 Algebraic Combinatorics, Lecture 23: Two combinatorial proofs of Cayley's formula
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18.212 S19 Algebraic Combinatorics, Lecture 24: Discussion of Problem Set 2
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18.212 S19 Algebraic Combinatorics, Lecture 25: Discussion of Problem Set 2 (cont.)
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18.212 S19 Algebraic Combinatorics, Lecture 26: Matrix Tree Theorem and more
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18.212 S19 Algebraic Combinatorics, Lecture 27: Matrix Tree Theorem (cont.) and more
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18.212 S19 Algebraic Combinatorics, Lecture 28: Proof of Matrix Tree Theorem using Cauchy-Binnet formula and more
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18.212 S19 Algebraic Combinatorics, Lecture 29: Proof of Directed Matrix Tree Theorem based on induction
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18.212 S19 Algebraic Combinatorics, Lecture 3: Pattern avoidance in permutations and more
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18.212 S19 Algebraic Combinatorics, Lecture 30: Proof of Directed Matrix Tree Theorem via the Involution Principle and more
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18.212 S19 Algebraic Combinatorics, Lecture 31: Electrical networks (cont.) and more
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18.212 S19 Algebraic Combinatorics, Lecture 32: Eulerian cycles in digraphs and B.E.S.T. theorem
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18.212 S19 Algebraic Combinatorics, Lecture 33: Parking functions and tree inversion polynomials
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18.212 S19 Algebraic Combinatorics, Lecture 34: Pascal triangle and more
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18.212 S19 Algebraic Combinatorics, Lecture 35: Lindstrom-Gessel-Viennot lemma and Lindstrom Theorem
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18.212 S19 Algebraic Combinatorics, Lecture 36: Proof of Lindstrom-Gessel-Viennot lemma and more
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18.212 S19 Algebraic Combinatorics, Lecture 37: MacMahon Proposition and more
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18.212 S19 Algebraic Combinatorics, Lecture 38: Discussion of Problem Set 3
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18.212 S19 Algebraic Combinatorics, Lecture 39: Plane partitions and more
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18.212 S19 Algebraic Combinatorics, Lecture 4: Frobenius-Young identity and more
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18.212 S19 Algebraic Combinatorics, Lecture 5: Proof of the hook-length formula based on a random hook walk
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18.212 S19 Algebraic Combinatorics, Lecture 6: Hook walks and more
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18.212 S19 Algebraic Combinatorics, Lecture 7: q-factorials and q-binomial coefficients
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18.212 S19 Algebraic Combinatorics, Lecture 8: Grassmannians over finite fields
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18.212 S19 Algebraic Combinatorics, Lecture 9: Sets and multisets. Statistics on permutations

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Spring 2019

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Undergraduate

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