Textbook |
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We will be using A Walk Through Combinatorics by Miklos Bona, supplemented by handouts as needed.
Scheduled Lectures |
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The course meets Mondays, Wednesdays, and Fridays from 1:45 – 2:50 in Haldeman 028.
Instructor |
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Vince Vatter |
Office: 314 Kemeny Hall |
Office hours: Monday 12:00 – 1:00, Tuesday 1:00 – 3:00, and 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(s) | Dates | Topics | Chapter |
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1 | Wednesday 9/23 | Binomial coefficients, unimodality, log-concavity | 4 |
2 | Friday 9/25 | Compositions
Homework #1 assigned (due on Wednesday) |
5 |
3 | Monday 9/28 | Set partitions | 5 |
4 | Wednesday 9/30 | Integer partitions | 5 |
5 | Friday 10/2 | Permutations and their cycles
Homework #2 assigned (due on Wednesday) |
6 |
6 | Monday 10/5 | Permutations and their cycles | 6 |
7 | Wednesday 10/7 | Posets: Dilworth's Theorem and Mirsky's Theorem | 16 |
8 | Friday 10/9 | The incidence algebra and Mobius inversion
Homework #3 assigned (due on Wednesday) |
16 |
9 | Monday 10/12 | Common Mobius functions | 16 |
10 | Wednesday 10/14 | Mobius functions of lattices; in particular the lattice of set partitions | 16 |
11 | Friday 10/16 | Sperner's theorem on antichains in the Boolean lattice and the Littlewood-Offord problem
Homework #4 assigned (due on Wednesday) |
16 |
12 | Monday 10/19 | Generating functions | 8 |
13 | Wednesday 10/21 | Rational generating functions | 8 |
14 | Friday 10/23 | Algebraic generating functions, and in particular, the Catalan numbers
Homework #5 assigned (due on Wednesday) |
8 |
15 | Monday 10/26 | Bootstrap percolation, the separable permutations, and the Schröder numbers | 8 |
16 | Wednesday 10/28 | Exponential generating functions (note: not covered on midterm) | 8 |
Wednesday 10/28 6:00–8:00pm |
Midterm in Kemeny 004 | ||
Friday 10/30 | Class cancelled (scheduled) | ||
17 | Monday 11/2 | Graphs and maximal independent sets | 9 |
Wednesday 11/4 | Class cancelled (due to flu) | ||
18 | Friday 11/6 | Graphs and maximal independent sets, continued Homework #6 assigned (due on Wednesday) |
9 |
19 | Monday 11/9 | The Max-Flow Min-Cut Theorem | n/a |
20 | Wednesday 11/11 | Baranyai's Theorem | n/a |
21 | Thursday 11/12 x-hour |
The Matrix-Tree Theorem | 10 |
22 | Friday 11/13 | The Matrix-Tree Theorem, continued;
note that there is a
much prettier proof of Cayley's formula
Homework #7 assigned (due on Wednesday) |
10 |
23 | Monday 11/16 | Groups, Permutation Groups, and Automorphism Groups | n/a |
24 | Wednesday 11/18 | Enumeration under group action (Póyla's Theorem) | n/a |
25 | Friday 11/20 | Enumeration under group action (Póyla's Theorem), continued | n/a |
26 | Monday 11/23 Thanksgiving recess begins Tuesday |
Combinatorial algorithms; for an entertainingly bad sorting algorithm, see here. | 17 |
27 | Monday 11/30 | Basics of computational complexity | n/a |
28 | Wednesday 12/2 | P vs. NP | n/a |
Friday 12/11 | Final exam is due |