Finding Structure in Sequences of Real Numbers via Graph Theory: a Problem List

We investigate a method of generating a graph \(G=(V,E)\) out of an ordered list of \(n\) distinct real numbers \(a_1, \dots, a_n\). These graphs can be used to test for the presence of interesting structure in the sequence. We describe sequences exhibiting intricate hidden structure that was discov...

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Bibliographic Details
Published in:arXiv.org 2021-09
Main Authors: Korssjoen, Dana G, Li, Biyao, Steinerberger, Stefan, Tripathi, Raghavendra, Zhang, Ruimin
Format: Article
Language:English
Subjects:
Graph theory
Real numbers
Online Access:Get full text
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Summary:We investigate a method of generating a graph \(G=(V,E)\) out of an ordered list of \(n\) distinct real numbers \(a_1, \dots, a_n\). These graphs can be used to test for the presence of interesting structure in the sequence. We describe sequences exhibiting intricate hidden structure that was discovered this way. Our list includes sequences of Deutsch, Erdős, Freud & Hegyvari, Recaman, Quet, Zabolotskiy and Zizka. Since our observations are mostly empirical, each sequence in the list is an open problem.
ISSN:2331-8422
DOI:10.48550/arxiv.2012.04625