Additive Number Theory - Extremal Problems and the Combinatorics of Sumsets by M. Nathanson

Additive Number Theory - Extremal Problems and the Combinatorics of Sumsets by M. Nathanson

International Centre for Theoretical Sciences via YouTube Direct link

Minimal asymptotic bases

23 of 24

23 of 24

Minimal asymptotic bases

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Additive Number Theory - Extremal Problems and the Combinatorics of Sumsets by M. Nathanson

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

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