Problems in additive number theory

Title: Problems in additive number theory
Identifier: d_2009_2013:9f3d0b979fda:10911
identifier: 11186
Creator: Ljujic, Zeljka,
Contributor: Melvyn B. Nathanson
Date: 2011
Language: English
Publisher: City University of New York.
Subject: Mathematics | Theoretical mathematics | Additive number theory | Combinatorics
Abstract: In the first chapter we obtain the Biro-type upper bound for the smallest period of B in the case when A is a finite multiset of integers and B is a multiset such that A and B are t-complementing multisets of integers. In the second chapter we answer an inverse problem for lattice points proving that if K is a compact subset of RxR such that K+ZxZ=RxR then the integer points of the difference set of K is not contained on the coordinate axes, Zx{lcub}0{rcub}∪{lcub}0{rcub}xZ. In the third chapter we show that there exist infinite sets A and M of positive integers whose partition function has weakly superpolynomial but not superpolynomial growth. The last chapter deals with the size of a sum of dilates 2·A+k·A. We prove that if k is a power of an odd prime or product of two primes and A a finite set of integers such that |A|>8k.;k,then |2· A+k·A|≥ ( k+2)|A|-k.;2-k+2.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics