English

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

Combinatorics 2022-08-10 v2

Abstract

We investigate a method of generating a graph G=(V,E)G=(V,E) out of an ordered list of nn distinct real numbers a1,,ana_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, Erd\H{o}s, Freud & Hegyvari, Recaman, Quet, Zabolotskiy and Zizka. Since our observations are mostly empirical, each sequence in the list is an open problem.

Keywords

Cite

@article{arxiv.2012.04625,
  title  = {Finding Structure in Sequences of Real Numbers via Graph Theory: a Problem List},
  author = {Dana G. Korssjoen and Biyao Li and Stefan Steinerberger and Raghavendra Tripathi and Ruimin Zhang},
  journal= {arXiv preprint arXiv:2012.04625},
  year   = {2022}
}
R2 v1 2026-06-23T20:49:28.125Z