A new class of minimal asymptotic bases

TL;DR

This paper introduces a new class of minimal asymptotic bases, expanding the understanding of how certain sets of integers can uniquely represent large numbers with minimal elements.

Contribution

It constructs a novel class of minimal asymptotic bases, providing new examples and insights into their structure and properties.

Findings

New class of minimal asymptotic bases constructed

Demonstrates the existence of diverse minimal bases

Enhances understanding of additive number theory

Abstract

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.