Linear Forms in Finite Sets of Integers

Han, Shu-Ping; Kirfel, Christoph; Nathanson, Melvyn B.

doi:10.1007/978-1-4757-4507-8_16

Search citation statements

Order By: Relevance

Paper Sections

Select...

Coloring the Integers2

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2000

2020

Publication Types

Select...

Article4

Other1

Relationship

Self Cite3

Independent2

Authors

Journals

Cited by 5 publications

(6 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The case t = 1 of the following theorem is the result of Han, Kirfel, and Nathanson [1]. The case q = 1 is Theorem 1.…”

Section: Coloring the Integersmentioning

confidence: 87%

See 1 more Smart Citation

Chromatic sumsets

Nathanson¹

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The case t = 1 of the following theorem is the result of Han, Kirfel, and Nathanson [1]. The case q = 1 is Theorem 1.…”

Section: Coloring the Integersmentioning

confidence: 87%

“…Han, Kirfel, and Nathanson [1] determined the asymptotic structure of homogeneous and inhomogeneous linear forms for all q-tuples of finite sets of integers.…”

Section: Coloring the Integersmentioning

confidence: 99%

Chromatic sumsets

Nathanson¹

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…. , A r and B are finite subsets of N 0 , normalized similarly as above, then Han, Kirfel, and Nathanson [2] showed that |B +…”

Section: Introductionmentioning

confidence: 96%

Algebraic Proof for the Geometric Structure of Sumsets

Lee

2011

Integers

View full text Add to dashboard Cite

We consider a finite set of lattice points and their convex hull. The author previously gave a geometric proof that the sumsets of these lattice points take over the central regions of dilated convex hulls, thus revealing an interesting connection between additive number theory and geometry. In this paper, we will see an algebraic proof of this fact when the convex hull of points is a simplex, exploring the connection between additive number theory and geometry further.

show abstract

“…. , h r sufficiently large, the structure of this "linear form" has also been completely determined (Han, Kirfel, and Nathanson [2]), and its cardinality is a linear function of h 1 , . .…”

Section: Introductionmentioning

confidence: 99%

Polynomial growth of sumsets in abelian semigroups

Nathanson¹,

Ruzsa²

2002

Journal De Théorie Des Nombres De Bordeaux

Self Cite

View full text Add to dashboard Cite

Let S be an abelian semigroup, and A a finite subset of S. The sumset hA consists of all sums of h elements of A, with repetitions allowed. Let |hA| denote the cardinality of hA. Elementary lattice point arguments are used to prove that an arbitrary abelian semigroup has polynomial growth, that is, there exists a polynomial p(t) such that |hA| = p(h) for all sufficiently large h. Lattice point counting is also used to prove that sumsets of the form h1A1 + • • • + hrAr have multivariate polynomial growth.

show abstract

Linear Forms in Finite Sets of Integers

Cited by 5 publications

References 7 publications

Chromatic sumsets

Chromatic sumsets

Algebraic Proof for the Geometric Structure of Sumsets

Polynomial growth of sumsets in abelian semigroups

Contact Info

Product

Resources

About