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Title: The postage stamp problem and arithmetic in base $r$ (English)
Author: Tripathi, Amitabha
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 4
Year: 2008
Pages: 1097-1100
Summary lang: English
Category: math
Summary: Let $h,k$ be fixed positive integers, and let $A$ be any set of positive integers. Let $hA:=\{a_1+a_2+\cdots +a_r\colon a_i \in A, r \le h\}$ denote the set of all integers representable as a sum of no more than $h$ elements of $A$, and let $n(h,A)$ denote the largest integer $n$ such that $\{1,2,\ldots ,n\} \subseteq hA$. Let $n(h,k):=\max _A\colon n(h,A)$, where the maximum is taken over all sets $A$ with $k$ elements. We determine $n(h,A)$ when the elements of $A$ are in geometric progression. In particular, this results in the evaluation of $n(h,2)$ and yields surprisingly sharp lower bounds for $n(h,k)$, particularly for $k=3$. (English)
Keyword: $h$-basis
Keyword: extremal $h$-basis
Keyword: geometric progression
MSC: 11B13
MSC: 11D04
idZBL: Zbl 1174.11013
idMR: MR2471168
Date available: 2010-07-21T08:11:21Z
Last updated: 2020-07-03
Stable URL:
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