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arXiv · 2301.04365

Lagrange-like spectrum of perfect additive complements

Balázs Bárány·Jin-Hui Fang·Csaba Sándor
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Abstract

Two infinite sets $A$ and $B$ of non-negative integers are called \emph{perfect additive complements of non-negative integers}, if every non-negative integer can be uniquely expressed as the sum of elements from $A$ and $B$. In this paper, we define a Lagrange-like spectrum of the perfect additive complements ($\mathfrak{L} $ for short). As a main result, we obtain the smallest accumulation point of the set $\mathfrak{L} $ and prove that the set $\mathfrak{L} $ is closed. Other related results and problems are also contained.

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Balázs Bárány, Jin-Hui Fang, Csaba Sándor. 2023-01-11. Lagrange-like spectrum of perfect additive complements. https://arxiv.org/abs/2301.04365

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