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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01422 |
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| _version_ | 1866908465086070784 |
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| author | De Paris, Alessandro |
| author_facet | De Paris, Alessandro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isomorphisms of graphs of Hyperbinary Expansions and Efficient Algorithms for Stern's Diatomic Sequence De Paris, Alessandro Combinatorics 11B83, 05C30, 68Q42, 68R01, 68R15 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. |
| title | Isomorphisms of graphs of Hyperbinary Expansions and Efficient Algorithms for Stern's Diatomic Sequence |
| topic | Combinatorics 11B83, 05C30, 68Q42, 68R01, 68R15 |
| url | https://arxiv.org/abs/2410.01422 |