UCLA Course: Math 285N, Fall 2022.
Instructor: Igor Pak
(see email instructions on the bottom of the page).
Class schedule: MWF 3:00-3:50 pm, MS 6201.
Office Hours: M 4:00-4:50
Grading: The grade will be based on attendance and class participation.
This is a topics course, with topics covering different aspects of the subject.
Supplementary reading materials:
- Domino tilings
- Combinatorial group theory
- Tilings with two bars
- Flip graph
- Height functions and extension theorems
- I. Pak, A. Sheffer and M. Tassy, Fast domino tileability (2016).
- A.V. Akopyan, A.S. Tarasov, A
constructive proof of Kirszbraun's theorem (2008), a clean proof of (discrete) Kirszbraun theorem
- U. Brehm,
Extensions of distance reducing mappings to
piecewise congruent mappings on Lm (1981), original article.
- (continuous) Kirszbraun theorem, Wikipedia.
- S.S. Tasmuratov, The bending
of a polygon into a polyhedron with a given boundary (1974), the oldest and most similar geometric result to that by Tassy.
- Ribbon tilings and rim hook bijection
- Murnaghan-Nakayama rule, Wikipedia.
- S.V. Fomin and D.W. Stanton, Rim hook lattices,
St. Peterburg Math Journal, 1997.
- I. Pak, Ribbon tile invariants, Trans. AMS (2000).
- C. Moore and I. Pak, Ribbon tile invariants from signed area, JCTA (2002).
- S. Sheffield, Ribbon tilings
and multidimensional height functions, Trans. AMS (2002).
- Matchings via identity testing
- Number of domino tilings
- L. Lovasz and M.D. Plummer, Matching Theory, Chapter 8.
- R. Kenyon, An introduction to the dimer model
- A. Kaufer, these notes
- N. Robertson, P.D. Seymour, R. Thomas, Permanents, Pfaffian orientations, and even directed circuits
- L. Pachter, Combinatorial
approaches and conjectures for 2-divisibility problems concerning domino tilings of polyominoes
- Tilings of rectangles
- Geometric tilings
- Counting tilings
Lecture notes for the course by Glenn Sun will be posted here (in .pdf).
to return to Igor Pak Home Page.
To e-mail me, click
here and delete .zzz
Put Math 285 in the Subject line.
Last updated 11/30/2022.