COMBINATORICS

Schedule.

Week 1.
  • Wednesday September 6th. Counting Spanning Trees.

    Week 2.
  • Monday September 11th. Enumerative Combinatorics.
  • Wednesday September 13th. Elementary Counting: multisets, multinomials.

    Week 3.
  • Monday September 18th. Inclusion-Exclusion and Mobius Inversion. [Problem Set 1 assigned.]
  • Wednesday September 20th. Stirling Numbers of the First Kind.

    Week 4.
  • Monday September 25th. Stirling Numbers of the Second Kind.
  • Wednesday September 27th. The Catalan Numbers. [Problem Set 1 due.]

    Week 5.
  • Monday October 2nd. Partitions of an Integer. [Problem Set 2 assigned.]
  • Wednesday October 4th. q-nomials: inversions; vector spaces; partitions.

    Week 6.
  • Monday October 9th. Holiday: Thanksgiving.
  • Tuesday October 10th. Posets: extremal set theory.
  • Wednesday October 11th. Posets: symmetric chain decompositions; order ideals. [Problem Set 2 due.]

    Week 7.
  • Monday October 16th. Posets: mobius inversion; lattices. [Problem Set 3 assigned.]
  • Wednesday October 20th. The Matrix Tree Theorem.

    Week 8.
  • Monday October 23rd. Generating Functions: the method.
  • Wednesday October 25th. Generating Functions: three classes of generating function. [Problem Set 3 due.]

    Week 9.
  • Monday October 30th. Generating Fuctions: proving combinatorial identities. [Problem Set 4 assigned.]
  • Wednesday November 1st. Generating Functions: the exponential formula.

    Week 10.
  • Monday November 6th. Generating Functions: the exponential formula (two variables).
  • Wednesday November 8th. Lagrange Inversion. [Problem Set 4 due.]

    Week 11.
  • Monday November 13th. Young Tableau. [Problem Set 5 assigned.]
  • Wednesday November 15th. Young Tableau: the hooklength formula.

    Week 12.
  • Monday November 20th. The Transfer Matrix Method.
  • Wednesday November 22nd. Generating Functions and Statistics. [Problem Set 5 due.]

    Week 13.
  • Monday November 27th. Inclusion-Exclusion. [Problem Set 6 assigned.]
  • Wednesday November 29th. Double Counting: Brouwer's Fixed Point Theorem.

    Week 14.
  • Monday December 4th. The Last Lecture. [Problem Set 6 due.]

    Week 15.
  • Monday December 11th. Final Exam 10am. (Room 1205)