Online ordering is currently unavailable due to technical issues. We apologise for any delays responding to customers while we resolve this. For further updates please visit our website: https://www.cambridge.org/news-and-insights/technical-incident
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 13 October 2016
Let 
$A$ be a subset of 
$\mathbb{N}$, the set of all nonnegative integers. For an integer 
$h\geq 2$, let 
$hA$ be the set of all sums of 
$h$ elements of 
$A$. The set 
$A$ is called an asymptotic basis of order 
$h$ if 
$hA$ contains all sufficiently large integers. Otherwise, 
$A$ is called an asymptotic nonbasis of order 
$h$. An asymptotic nonbasis 
$A$ of order 
$h$ is called a maximal asymptotic nonbasis of order 
$h$ if 
$A\cup \{a\}$ is an asymptotic basis of order 
$h$ for every 
$a\notin A$. In this paper, we construct a sequence of asymptotic nonbases of order 
$h$ for each 
$h\geq 2$, each of which is not a subset of a maximal asymptotic nonbasis of order 
$h$.
You have
Access
