A NOTE ON ASYMPTOTIC NONBASES
2016 ◽
Vol 95
(1)
◽
pp. 1-4
Keyword(s):
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 $h$.
1984 ◽
Vol 17
(24)
◽
pp. L891-L895
◽
2018 ◽
Vol 97
(3)
◽
pp. 363-366
2011 ◽
Vol 84
(1)
◽
pp. 40-43
◽
Keyword(s):
2004 ◽
Vol 2004
(30)
◽
pp. 1589-1597
◽
Keyword(s):
2019 ◽
Vol 15
(02)
◽
pp. 389-406
◽
2008 ◽
Vol 27
(3)
◽
pp. 638-650
◽
Keyword(s):
Keyword(s):
2018 ◽
Vol 14
(04)
◽
pp. 919-923
◽