To successfully complete this assignment, you are supposed to write a summary of one of the articles listed below. You choose which one. If you don't like the list, you are most welcome to suggest another article. It should, however, not be one which you are already familiar with!

I don't want to specify how long the summary should be, but 500 words are probably too few and 5000 are certainly too many.

The intended reader has your background in mathematics but has not read the article. Important things that (s)he wants to know are:

• What is the motivation for the article to exist? In what context does the article fit?
• What are the main results? Why are they important? (Or, why are they not important?)
• How do the proofs go? Main ideas and techniques? Sketch important proofs but leave out tedious details that you find less significant.
• Your (motivated) opinion on the article? Well-presented or not? Important or not? Interesting or not? What is good? What is bad?

The deadline is Jan 16, 2016. You may send it by email or leave it in my mailbox at KTH. If your summary is almost, but not quite, satisfactory you will get a chance to fix it.

The articles:

1. R. P. Stanley, Two poset polytopes

2. M. Bona, Permutations with one or two 132-subsequences

3. J. Hallam, B. Sagan, Factoring the characteristic polynomial of a lattice

4. M. Skandera, A characterization of (3+1)-free posets

5. A. Claesson, S. Linusson, n! matchings, n! posets

6. M. Dukes, V. Jelínek, M. Kubitzke, Composition matrices, (2+2)-free posets and their specializations

7. R. Ehrenborg, E. Steingrímsson, The excedance set of a permutation

8. B. E. Tenner, A non-messing-up phenomenon for posets

9. I. Gessel, G. Viennot, Binomial Determinants, Paths and Hook Length Formulae

10. S. Fomin, A. Zelevinsky, Total Positivity: Tests and parametrization

11. E. R. Canfield, H. S. Wilf, Counting permutations by their alternating runs