Vol. 15, No. 2, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 2, 185–365
Issue 1, 1–184

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
Finding structure in sequences of real numbers via graph theory: a problem list

Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi and Ruimin Zhang

Vol. 15 (2022), No. 2, 251–270
Abstract

We investigate a method of generating a graph G = (V,E) out of an ordered list of n distinct real numbers a1,,an. These graphs can be used to test for the presence of combinatorial structure in the sequence. We describe sequences exhibiting intricate hidden structure that was discovered this way. Our list includes sequences of Deutsch, Erdős, Freud and Hegyvari, Recamán, Quet, Zabolotskiy and Zizka. Since our observations are mostly empirical, each sequence in the list is an open problem.

Keywords
integer sequence, spectral gap, OEIS
Mathematical Subject Classification
Primary: 05C90, 06A99
Milestones
Received: 18 January 2021
Revised: 6 September 2021
Accepted: 9 September 2021
Published: 29 July 2022

Communicated by Joshua Cooper
Authors
Dana G. Korssjoen
Department of Mathematics
University of Washington
Seattle, WA
United States
Biyao Li
Department of Mathematics
University of Washington
Seattle, WA
United States
Stefan Steinerberger
Department of Mathematics
University of Washington
Seattle, WA
United States
Raghavendra Tripathi
Department of Mathematics
University of Washington
Seattle, WA
United States
Ruimin Zhang
Department of Mathematics
University of Washington
Seattle, WA
United States