The postage stamp problem and arithmetic in base $r$

Tripathi, Amitabha. "The postage stamp problem and arithmetic in base $r$." Czechoslovak Mathematical Journal 58.4 (2008): 1097-1100. <http://eudml.org/doc/37888>.

@article{Tripathi2008,
abstract = {Let $h,k$ be fixed positive integers, and let $A$ be any set of positive integers. Let $hA:=\lbrace a_1+a_2+\cdots +a_r\colon a_i \in A, r \le h\rbrace $ 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 $\lbrace 1,2,\ldots ,n\rbrace \subseteq hA$. 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 $k=3$.},
author = {Tripathi, Amitabha},
journal = {Czechoslovak Mathematical Journal},
keywords = {$h$-basis; extremal $h$-basis; geometric progression; -basis; extremal -basis; geometric progression},
language = {eng},
number = {4},
pages = {1097-1100},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The postage stamp problem and arithmetic in base $r$},
url = {http://eudml.org/doc/37888},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Tripathi, Amitabha
TI - The postage stamp problem and arithmetic in base $r$
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1097
EP - 1100
AB - Let $h,k$ be fixed positive integers, and let $A$ be any set of positive integers. Let $hA:=\lbrace a_1+a_2+\cdots +a_r\colon a_i \in A, r \le h\rbrace $ 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 $\lbrace 1,2,\ldots ,n\rbrace \subseteq hA$. 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 $k=3$.
LA - eng
KW - $h$-basis; extremal $h$-basis; geometric progression; -basis; extremal -basis; geometric progression
UR - http://eudml.org/doc/37888
ER -