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. InclusionExclusion 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. qnomials: 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. InclusionExclusion. [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)