Topics in Discrete mathematics/Number theory

Christian Elsholtz
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

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.