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Additive Number Theory - Extremal Problems and the Combinatorics of Sumsets by M. Nathanson
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- 1 Additive Number Theory: Extremal Problems and the Combinatorics of Sumsets
- 2 Sumsets in groups
- 3 For subsets AI, ..., An of G, define the sumset
- 4 Simple questions
- 5 Simple questions
- 6 Density of sets and sumsets of integers
- 7 Lower bounds for sums of finite sets
- 8 We ave similar bounds for sets of congruence classes
- 9 There are many proofs. Here is an elementary proof that uses the "polynomial method."
- 10 Lemma
- 11 Lemma - If A and are subsets of a finite set G, then
- 12 Lemma - Let A and be subsets of a finite abelian group G.
- 13 Theorem Cauchy-Davenport
- 14 Because
- 15 Lemma
- 16 Theorem
- 17 Consider the monomial xmyn.
- 18 Theorem Dias da Silva-Hamidoune
- 19 References
- 20 Extremal properties of additive bases
- 21 Erdos-Turan conjecture
- 22 Thin bases - An asymptotic basis A of order is thin if
- 23 Minimal asymptotic bases
- 24 Idea 1970: If the Erdos-Turan conjecture were false,
