**Combinatorics (Math 4707), Spring 2018**

Darij Grinberg (203B Vincent Hall)

**Main resources:**

**This site is moving to https://www.cip.ifi.lmu.de/~grinberg/t/18s/ !** Please change your links and references.

Quick book references (*italics* = free):
Loehr (errata);
*Graham/Knuth/Patashnik (errata)*;
*Bogart*;
Bóna;
*Galvin*;
*Lehman/Leighton/Meyer*.

Basics on equivalence relations and equivalence classes: class materials by Melissa Lynn and by Jonathan Rogness (part 1 and part 2).

Extra notes: Network flows (sourcecode); this includes definitions of simple digraphs and multidigraphs.

See Math 5707 from Spring 2017 for some graph theory, specifically lecture 9 for trees and their many definitions.

See Math 4707 from Fall 2017 for some solved exercises.

"Black"board writing:

- Jan 17 | Jan 22 | Jan 24 | Feb 5 | Feb 7 | Feb 12 | Feb 14 | Feb 19 | Feb 21 | Feb 26 | Mar 5 | Mar 19 | Mar 21 | Mar 26 | Mar 28 | Apr 2 | Apr 4 | Apr 9 | Apr 11 | Apr 23 | Apr 25 (references) | Apr 30 | May 2 |

(Jan 29: Vic Reiner was substituting, talking about Inclusion/Exclusion and the Multinomial Formula. See Sections 16 of *Galvin* for the former and the WP for the latter.)

(Fri 28: Vic Reiner was substituting, talking about Catalan numbers.)

(Mar 7: Vic Reiner was substituting, talking about generating functions.)

**Homework and other problems:**

A LaTeX template for those who want to write their solutions in LaTeX. (Compiled PDF.)

- Homework set 1 (TeX source). Solutions (TeX source).
- Homework set 2 (TeX source). Solutions (TeX source).
- Midterm 1 (TeX source). Solutions (TeX source). Solutions to Exercises 1, 4 and 5 by Brady Olson.
- Homework set 3 (TeX source). Solutions (TeX source). Solutions to Exercises 1, 3 and 5 by Nathaniel Gorski.
- Further reading (TeX source), including applications, history and challenge problems.
- Midterm 2 (TeX source). Solutions to Exercises 1, 2 and 3 (TeX source). Solutions to Exercises 1, 3, 4 and 6 by Nathaniel Gorski. Solutions to Exercises 1, 5 and 6 by Brady Olson.
- Homework set 4 (TeX source). Solutions (TeX source). Solutions to Exercises 1 and 4 by Nathaniel Gorski.
- Homework set 5 (TeX source). Provisional solutions (TeX source).
- Midterm 3 (TeX source). Solutions to Exercises 1 and 3a (TeX source). Solutions to Exercises 1, 2 and 4 by Nathaniel Gorski. Solutions to Exercises 1, 2 and 5 by James Hirsch.
- Average scores.

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