HSE
Math in Moscow
Math in Moscow schedule

Combinatorics (spring 2012)

Joint course with the Math in Moscow program

(teacher Yu.Burman)

Lectures

• Lecture 1: Binomial coefficients.
• Lectures 2 and 3: Linear recursion.
• Lecture 4: Catalan numbers.
• Lecture 5: Symmetric group.
• Lecture 6: Partitions.
• Lecture 7: Lagrange inversion and tree enumeration.
• Lecture 8: Parking functions.
• Lecture 9: Tutte polynomial.
• Lectures 10 and 11: Jacobi and Rogers–Ramanujan.

Problems and homeworks

• Problem set 1: Generating functions.
  Homework 1 (due February 13): Problems 1.1, 1.2a and 1.3.
• Problem set 2: Linear recursion.
  Homework 2 (due February 20): Problem 2.2 and any one problem from the set 1.
  Homework 3 (due February 27): Problems 2.1 and 2.3.
• Problem set 3: Catalan numbers. (differs from the one given in class!)
  Attention: no class on March 5 due to St.Petersburg excursion.
  Homework 4 (due March 12): all of Set 3.
  Homework 5 (due March 26): the unsolved problems of the midterm exam.
• Problem set 4: Symmetric group.
  Homework 6 (due April 2): all of Set 4.
• Problem set 5: Partitions and q-binomial coefficients.
  Homework 7 (due April 9): Problems 5.2 and 5.3a; also Problem 5.1d if you can.
• Problem set 6: Trees.
  Homework 8 (due April 16): all of Set 6, and redo 5.2 if necessary.
• Problem set 7: Parking functions.
  Homework 9 (due April 23): Set 7, except 7.2b and 7.2c.
• Problem set 8: Tutte polynomial.
  Homework 10 (due April 30): Set 8.
• Problem set 9: Exclusion-inclusion.
  Homework 11 (due May 7): Set 9.

Exams

• Midterm exam.