论文标题

一类新的最小渐近基础

A new class of minimal asymptotic bases

论文作者

Nathanson, Melvyn B.

论文摘要

如果每个足够大的整数都可以表示为$ h $的总和,则不一定是$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ h $的渐近基础。如果删除$ a $的任何元素会破坏无限多个整数的每个代表,那么渐近基$ a $是最小的,因此,$ a \ setminus \ {a \} $不是$ a \ in a $的所有$ a \的订单$ h $的渐近基础。在本文中,建立了新的最小渐近基碱。

A set $A$ of nonnegative integers is an asymptotic basis of order $h$ if every sufficiently large integer can be represented as the sum of $h$ not necessarily distinct elements of $A$. The asymptotic basis $A$ is minimal if removing any element of $A$ destroys every representation of infinitely many integers, and so $A\setminus \{a\}$ is not an asymptotic basis of order $h$ for all $a\in A$. In this paper, a new class of minimal asymptotic bases is constructed.

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