Courses:

Algebraic Combinatorics >> Content Detail



Syllabus



Syllabus


Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.


Prerequisites


Linear Algebra (18.700) or Algebra I (18.701)



Recommended Textbooks


Amazon logo van Lint, J. H., and R. M. Wilson. A Course in Combinatorics. Cambridge, U.K.: Cambridge University Press, 1992. ISBN: 0521422604. (Reprinted 1994, 1996.)

Stanley, R. P., Sergey Fomin, B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak, and B. Simon. Course notes on Topics in Algebraic Combinatorics.

Amazon logo ———. Enumerative Combinatorics. Vol. 1 and 2. Cambridge, U.K.: Cambridge University Press, 2001. ISBN: 0521789877.



Topics


  • Catalan Numbers, Triangulations, Catalan Paths, Noncrossing Set Partitions

  • Symmetric Group, Statistics on Permutations, Inversions and Major Index

  • Partially Ordered Sets and Lattices, Sperner's and Dilworth's Theorems

  • Young's Lattice, Tableaux, and Schensted's Correspondence

  • q-Binomial Coefficients, Gaussian Coefficients, and Young Diagrams

  • Partitions, Euler's Pentagonal Theorem, Jacobi Triple Product

  • Noncrossing Paths, Lindstrom Lemma (Gessel-Viennot Method)

  • Matrix-Tree Theorem, Electrical Networks, Walks in Graphs

  • Lattice Paths and Continued Fractions

  • Transportation and Birkhoff Polytopes, Cyclic Polytopes, Permutohedra

  • Matching Enumeration, Pfaffians, Ising Model, Domino Tilings


Grading


Based on the 4 assignments.


 








© 2017 Coursepedia.com, by Higher Ed Media LLC. All Rights Reserved.