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Algebraic Proof for the Geometric Structure of Sumsets
Veröffentlicht/Copyright:
4. August 2011
Abstract
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.
Received: 2010-01-26
Revised: 2010-10-25
Accepted: 2011-02-03
Published Online: 2011-08-04
Published in Print: 2011-August
© de Gruyter 2011
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Artikel in diesem Heft
- The Number of Solutions of λ(x) = n
- Monochromatic Sums Equal to Products in ℕ
- On the Sum of Reciprocal Generalized Fibonacci Numbers
- Recursively Self-Conjugate Partitions
- Modular Hyperbolas and the Coefficients of (x–1 + 6 + x)k
- Algebraic Proof for the Geometric Structure of Sumsets
- An Erdős–Fuchs Type Theorem for Finite Groups
- Coincidences of Catalan and q-Catalan Numbers
- Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
- Remarks on the Pólya–Vinogradov Inequality
- Heights of Divisors of xn – 1
- Bernoulli Numbers and Generalized Factorial Sums
- Witten Volume Formulas for Semi-Simple Lie Algebras
Artikel in diesem Heft
- The Number of Solutions of λ(x) = n
- Monochromatic Sums Equal to Products in ℕ
- On the Sum of Reciprocal Generalized Fibonacci Numbers
- Recursively Self-Conjugate Partitions
- Modular Hyperbolas and the Coefficients of (x–1 + 6 + x)k
- Algebraic Proof for the Geometric Structure of Sumsets
- An Erdős–Fuchs Type Theorem for Finite Groups
- Coincidences of Catalan and q-Catalan Numbers
- Phase Transitions in Infinitely Generated Groups, and Related Problems in Additive Number Theory
- Remarks on the Pólya–Vinogradov Inequality
- Heights of Divisors of xn – 1
- Bernoulli Numbers and Generalized Factorial Sums
- Witten Volume Formulas for Semi-Simple Lie Algebras
