Topics in Combinatorics IV

Michaelmas 2026

Time and place:	Lectures:	Mon 17:00 CG218, Wed 11:00 E245
	Problems classes:	Fri 11:00 CG218, Weeks 2,4,6,8

Instructor: Pavel Tumarkin
e-mail: pavel dot tumarkin at durham dot ac dot uk
Office: MCS3009; Phone: 334-3085
Office hours: Tue 16:30-17:30 and by appointment

Textbooks:

Richard P. Stanley, Enumerative combinatorics, vol.1, vol.2 (the access is free from DU network)

Parts of the content of the first term can also be found in the following books:

Richard P. Stanley, Catalan numbers.
Bruce E. Sagan, The symmetric group: representations, combinatorial algorithms, and symmetric functions.

Preliminary course content (subject to change): Catalan numbers, partitions and Young diagrams, set partitions, statistics on permutations, posets and lattices, Robinson-Schensted correspondence, pattern avoidance in permutations

Schedule:

Week 1: Catalan numbers: definitions, examples, generating function

Week 2: Catalan numbers: further examples; partitions and Young diagrams. Problems class

Week 3: The hook length formula

Week 4: Set partitions. Problems class

Week 5: Exponential formula; statistics on permutations

Week 6: Partially ordered sets. Problems class

Week 7: Posets and lattices

Week 8: Linear extensions of posets; Robinson-Schensted correspondence. Problems class

Week 9: Properties of RSK

Week 10: Symmetries of RSK; pattern avoidance in permutations

Handouts: (lecture notes, intended to be more or less up to date)

Catalan numbers

Problems classes:

Homeworks: There will be weekly homework assignments. Selected exercises are to be handed in on Fridays of weeks 3, 5, 7, and 9 via Gradescope