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arXiv · 2410.01422

Isomorphisms of graphs of Hyperbinary Expansions and Efficient Algorithms for Stern's Diatomic Sequence

Alessandro De Paris
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Abstract

To investigate hyperbinary expansions of a nonnegative integer~$n$, an edge-labeled directed graph $A(n)$ has recently been introduced. After pointing out some new simple facts about its cyclomatic number, we give a relatively simple description of its structure and prove that if $m,n$ are even numbers for which $A(n)$ and $A(m)$ are isomorphic as edge-labeled graphs, then $m=n$. From the structure of $A(n)$ we also derive a formula related to Stern's diatomic sequence, and in the same vein discuss some algorithms that recently appeared in the literature.

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Alessandro De Paris. 2024-10-02. Isomorphisms of graphs of Hyperbinary Expansions and Efficient Algorithms for Stern's Diatomic Sequence. https://doi.org/10.1007/s41980-026-01063-w

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