On some problems in Additive number theory
Material type: TextPublication details: 2005Description: 64pSubject(s): Mathematics | Algebra | Sum-free setsOnline resources: Click here to access online Dissertation note: 2005Ph.DOthers Abstract: This thesis discusses some problems relating the properties of a set A and those of A+A, when A is a subset of an abelian group. Given a finite abelian group G and A is a subset of G, it is said that A is sum-free if the sets 2A and A are disjoint. Chapter 2 discusses the problem of finding the structure of all large sum-free subsets of G. The complete structure of all largest sum-free subsets of G, are obtained provided all the divisors of order G are congruent to 1 modulo 3. Also partial results are obtained regarding structure of all large maximal sum-free subsets of G. A sum-free set A is maximal if it is not a proper subset of any sum-free set. If there is a divisor of order of G which is not congruent to 1 modulo 3 then structure of all largest sum-free subsets of G was known before. The results in this thesis are based on a recent result of Ben Green and Imre Ruzsa. Chapter 3 improves the 'error term' in asymptotic formula of sigma (G) obtained by Ben Green and Imre Ruzsa, using slight refinement of the methods. Chapter 4 discusses a problem on an additive representation function, using an additive lemma proven by means of graph theory.Current library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available |
2005
Ph.D
Others
This thesis discusses some problems relating the properties of a set A and those of A+A, when A is a subset of an abelian group. Given a finite abelian group G and A is a subset of G, it is said that A is sum-free if the sets 2A and A are disjoint. Chapter 2 discusses the problem of finding the structure of all large sum-free subsets of G. The complete structure of all largest sum-free subsets of G, are obtained provided all the divisors of order G are congruent to 1 modulo 3. Also partial results are obtained regarding structure of all large maximal sum-free subsets of G. A sum-free set A is maximal if it is not a proper subset of any sum-free set. If there is a divisor of order of G which is not congruent to 1 modulo 3 then structure of all largest sum-free subsets of G was known before. The results in this thesis are based on a recent result of Ben Green and Imre Ruzsa. Chapter 3 improves the 'error term' in asymptotic formula of sigma (G) obtained by Ben Green and Imre Ruzsa, using slight refinement of the methods. Chapter 4 discusses a problem on an additive representation function, using an additive lemma proven by means of graph theory.
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