enumerative combinatorics
san francisco state university
federico ardila
2013

. eccc . homework . lectures . people . projects . syllabus . texts .

O homework assignments

hw 1 (due sep 6)
hw 2 (due sep 20)
hw 3 (due oct 4)
hw 4 (due oct 17)

O homework solutions

homework 1

1 (hayden)
2abc (hannah)
2d (felipe s)
2d (jorge)
3 (servando)
4 (emily)
5 (david a)
5 (victor)
6 (david k)

homework 2

1 (kyla)
1d (david k)
2 (crista)
3 (jose)
3b (brian c)
3b (federico c)
4 (fabian)
5 (nicolas)
6 (david a)

Note: I discovered Problem 5 when learning about Hall-Littlewood functions and the "charge of a permutation". I suggested this project to Igor Kortchemski (then a high school student!), who wrote this nice paper about this topic.

homework 3

1 (david pa)
2 (felipe)
2 (alejandro)
3 (brian c)
3 (jorge)
3 (federico a) -- see Cor. 3.5 and Th. 3.6
4 (andres r)
5 (david pa)
5 (matthew)

Problem 6 is called the Jacobi identity; there are at least two different combinatorial proofs by Zolnowski and Vershik.

homework 4

1 (julian)
1 (servando)
2 (david k)
3 (jose)
4 (nina)

The sequences of polynomials satisfying the equation of problem 2 are called "of binomial type". Here are a basic discussion on these sequences (including the foundational references) is here and a description of some very nice recent news by undergraduate Jon Schneider. You'll see there is more to do!

Problem 6 was first proposed by Conway in his paper "The Weird and Wonderful Chemistry of Audioactive Decay". I remember this is a fun paper, but maybe not worth the \$29.95 that Springer wants me to pay to download it (and probably not be allowed to post it on this webpage). Unfortunately the SFSU library doesn't have it, maybe Los Andes does. If anyone is very interested, I am happy to try to dig up an old photocopy I made years ago, which should be in my office somewhere. In the meantime, you can see analyses of the problem by the computer/human team of Ekhad and Zeilberger, by Litherland and his computer, or by Johnston and his computer.

short hw 1: felipe . julian . matt

short hw 2: brian c . julian

short hw 3: david a . felipe