Institut für Analysis und Zahlentheorie

Sommersemester 2016

About every 2 weeks exercise class, usually on Tuesday

Here are the exercise sheets

No 1

No 2

No 3

No 4

Topics

1) Arrow theorem, a survey on judgment aggregation

2) Thue-Morse sequence, almost periodic sequences

(1-2 following Jacobs Einführung in die Kombinatorik)

3) Sumsets, Cauchy-Davenport theorem

(3 following somewhat Natahnson, additive number theory, inverse problems...)

4) Combinatorial Nullstellensatz (Noga Alon's paper)

restricted set addition, Erdös-Heilbronn conjecture

Erdös-Ginzburg-Ziv, Reiher's solution of Kemnitz conjecture and the multidimensional case

Croot-Lev-Pach paper on Z_4^n, cap sets

Salem-Spencer/Behrend paper on integers without arithmetic progressesions

Construction of progression free sets

Universal sequences (On strings containing all subsets as substringsOriginal, Discrete Mathematics, Volume 21, Issue 3, 1978, Pages 253-259 Witold Lipski Jr.)

Sperner's Lemma (following Jukna's book)

LYM inequality

Paper by Fox and Lovasz on regularity lemma (arXiv:1606.01230)

Varnavides in integers and in vector spaces.