Textbook |
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There is no official textbook for this course. The textbooks from which the lectures will be planned, which may be helpful as resources, are:
Scheduled Lectures |
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The course meets Tuesday and Thursday from 10:00 – 11:50 in Kemeny 201. (We will take a 10 minute break roughly in the middle of each lecture.)
Note that the "Thursday Lunch Expedition" immediately follows the Thursday lectures, and that this is in turn followed by the Combinatorics Seminar.
The x-hour is Wednesday 3:00 – 3:50, but its use is not anticipated.
Instructor |
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Vince Vatter |
Office: 314 Kemeny Hall |
Office hours: by appointment |
Phone: 646-3507 |
Blitzmail: vincent.vatter (preferred) |
Grades |
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The Honor Principle |
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Very Rough Draft of Tentative Schedule |
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Lecture | Date | Topics |
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1 | Tuesday 3/31 | Overview of combinatorics, also counting Supplemental reading: Enumerative and algebraic combinatorics, What is an answer? |
2 | Thursday 4/2 | Derangements, permanents, involutions, and the Erdos-Szekeres Theorem |
3 | Tuesday 4/7 | Inclusion-exclusion, the Bell numbers, the Stirling numbers |
4 | Thursday 4/9 | Hall's marriage theorem and the number of Latin squares of order n |
5 | Tuesday 4/14 | The proof of Evans' Conjecture: If at most n-1 cells of an n by n array
are filled (with no repetitions in the rows or columns), then the array can be extended to a Latin
square of order n. Homework #1 assigned |
6 | Thursday 4/16 | Posets, and the theorems of Dilworth, Mirsky, and Sperner |
7 | Tuesday 4/21 | Downsets, especially in |
8 | Thursday 4/23 | The Fundamental Theorem of Finite Distributive Lattices Homework #2 assigned |
9 | Tuesday 4/28 | Mobius inversion |
10 | Thursday 4/30 | Dimension Theory for posets |
11 | Tuesday 5/5 | Rational generating functions Homework #3 assigned |
12 | Thursday 5/7 | Algebraic and D-finite generating functions |
13 | Tuesday 5/12 | Formal languages |
14 | Thursday 5/14 | Permutation patterns |
15 | Tuesday 5/19 | Permutation patterns
Homework #4 assigned |
16 | Thursday 5/21 | Guest lecture by Prof. Peter Winkler on the probabilistic method |
17 | Tuesday 5/26 | The Combinatorial Nullstellensatz |
18 | Thursday 5/28 | The Combinatorial Nullstellensatz |