Vol. 12, No. 3, 2019

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Rigidity of Ulam sets and sequences

Joshua Hinman, Borys Kuca, Alexander Schlesinger and Arseniy Sheydvasser

Vol. 12 (2019), No. 3, 521–539
Abstract

We give a number of results about families of Ulam sequences and sets, further exploring recent work on rigidity phenomena. For Ulam sequences, using elementary methods we give an upper bound on the density and prove regularity for various families of sequences. For Ulam sets, we consider extensions of classification work done by Kravitz and Steinerberger.

Keywords
Ulam sequence, additive number theory
Mathematical Subject Classification 2010
Primary: 11B83, 11P70
Secondary: 05A16
Milestones
Received: 10 July 2018
Revised: 31 July 2018
Accepted: 5 September 2018
Published: 14 December 2018

Communicated by Kenneth S. Berenhaut
Authors
Joshua Hinman
Department of Mathematics
Yale University
New Haven, CT
United States
Borys Kuca
School of Mathematics
University of Manchester
Manchester
United Kingdom
Alexander Schlesinger
Department of Mathematics
Yale University
New Haven, CT
United States
Arseniy Sheydvasser
Department of Mathematics
The Graduate Center
New York, NY
United States