Geodesic
On Minimal Asymptotic Bases
Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 887-894

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Let $\mathbb N$ denote the set of all nonnegative integers, and let $A\subseteq\mathbb N$. Let $h,n\in\mathbb N$, $h\ge 2$ and $r_h(A,n)=\#\{(a_1,\dots,a_h)\in A^h:a_1+\dotsb+a_h=n\}$. The set $A$ is called an asymptotic basis of order $h$ if $r_h(A,n)\ge 1$ for all sufficiently large integer $n$. An asymptotic basis $A$ of order $h$ is minimal if no proper subset of $A$ is an asymptotic basis of order $h$. Recently, Sun used 2-adic representations of integers to construct a new class of minimal asymptotic bases of order $h$. In this paper, we generalize the 2-adic result to the $g$-adic case.
Keywords: minimal asymptotic basis, $g$-adic representation.
Mots-clés : partition 
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     author = {C.-F. Sun and Zhi Cheng},
     title = {On {Minimal} {Asymptotic} {Bases}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {111},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a7/}
}
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C.-F. Sun; Zhi Cheng. On Minimal Asymptotic Bases. Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 887-894. http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a7/