Aspects of Combinatorics and Combinatorial Number Theory

3.1 of Chapter a₁ additive number theory Alon and Dubiner arithmetic progression assume b₁ b₂ c₁ coefficient compact semigroup congruent conjecture consider contains corresponding defined DEFINITION denote the number distinct dots elements equation Erdős Erdős-Ginzburg-Ziv Theorem Exercises from Chapter exists finite colouring finite set finite subsets fliptop Furstenberg and Katznelson graph G graphical representation Hales-Jewett theorem hence idempotent implies induction k-subsets least left ideal Lemma length matrix minimal left ideal modulo monochromatic monochromatic solution monomial N₁ non-empty subsets notations NU(V number of partitions observe obtained partition function pigeonhole principle points polynomial posets positive integer prime prove r-colouring Rado Ramsey Theory Ramsey-type Ramsey's theorem real numbers REMARK result Rödl Sárközy Schur's theorem Section self-conjugate semigroup sequence a1 Shelah Sidon set T₁ Theorem 2.1 theorem Theorem triangle vector vertices Waerden's theorem y₁ Z+)d