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arXiv · 1711.00145

The Unreasonable Rigidity of Ulam Sets

Joshua Hinman·Borys Kuca·Alexander Schlesinger·Arseniy Sheydvasser
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Abstract

We give a number of results about families of Ulam sets. Generalizing behavior of Ulam sets U(1,n), we prove using an novel model theoretic approach that there is a rigidity phenomenon for Ulam sets U(a,b) as b increases. Based on this, we suggest a natural conjecture, and investigate its potential applications, including a method of proving certain families of Ulam sequences are regular, for which we also provide partial, unconditional, results. Along this same vein, we give an upper bound bound on the density of Ulam sequences U(1,n). Finally, we give classification results for higher dimensional Ulam sets.

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Joshua Hinman, Borys Kuca, Alexander Schlesinger, Arseniy Sheydvasser. 2017-10-31. The Unreasonable Rigidity of Ulam Sets. https://arxiv.org/abs/1711.00145

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