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Algebraic Combinatorics >> Content Detail



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Calendar

Lec #TopicsKey dates
1Catalan Numbers
2Pattern Avoidance in Permutations, Young Tableaux, Schensted Correspondence, Longest Increasing Subsequences
3The Hooklength Formula

Random Hook Walks

A "Hooklength Formula" for Increasing Trees
4q-analogues, q-binomial Coefficients, q-factorials
5Symmetric Group, Statistics on Permutations, Inversions and Major Index
6Posets, Lattices, Distributive Lattices, Young's Lattice, Differential Posets
7Up and Down Operators, Unimodality of Gaussian Coefficients
8Sperner's and Dilworth's TheoremsProblem set 1 due
9De Bruijn Sequences
10Partitions: Euler's Pentagonal Theorem, Jacobi Triple Product
11Lindstrom Lemma (Gessel-Viennot Method)

Exponential Formula
12Weighted Lattice Paths and Continued FractionsProblem set 2 due
13Review of Problem Set 1
14Review of Problem Set 2
15Cayley's Formula, Prufer's Codes, Egecioglu and Remmel's Bijection
16Spanning Trees, Matrix-Tree Theorem, Directed Matrix-Tree TheoremProblem set 3 due
17Electrical NetworksProblem set 4 due
18Review of Problem Set 3
19BEST Theorem

Permutohedra, Newton Polytopes, Zonotopes
20Domino Tilings of Rectangles
21Birkhoff Polytope and Hall's Marriage Theorem
22Pfaffians and Matching Enumeration, Ising Model
23Plane Partitions, Rhombus Tilings of Hexagon, Pseudoline Arrangements
24Review of Problem Set 4
25Eulerian Numbers and Hypersimplices
26What Next?

 








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