Result: Representing Powers of Numbers as Subset Sums of Small Sets: Representing powers of numbers as subset sums of small sets
Title:
Representing Powers of Numbers as Subset Sums of Small Sets: Representing powers of numbers as subset sums of small sets
Authors:
Source:
Journal of Number Theory. 89:193-211
Publisher Information:
Elsevier BV, 2001.
Publication Year:
2001
Subject Terms:
subset sums, number theory, Algebra and Number Theory, Additive number theory, partitions, rank of geometric progressions of integers, combinatorics, Other combinatorial number theory, upper and lower bounds, 0103 physical sciences, representations of numbers, 0102 computer and information sciences, 01 natural sciences
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0022-314X
DOI:
10.1006/jnth.2000.2646
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....a8e8e779ec1b05205b3a4102a8314168
Database:
OpenAIRE
Further Information
If \(A,B\subset \mathbb{R}\), \(B\) is said to represent \(A\) if for any \(a\in A\), there is a \(C\subset B\) such that \(a= \sum_{c\in C}c\). The rank of \(A\) is, by definition, the minimal cardinality of a set \(B\) that represents \(A\). For instance, \(\text{rk}(\{1,2,4,8,16\})\leq 4\) because \(\{1,2,4,8,16\}\) is represented by \(\{-5,1,7,9\}\). The paper under review presents nontrivial upper and lower bounds of the rank of geometric progressions of integers.