Hiccup sequences, a Kimberling's conjecture, and Dumont-Thomas numeration systems

Abstract: This is part of a joint work with Robbert Fokkink (TU Delft). We generalise the self-referential sequences introduced by Benoit Cloitre in 2003 on OEIS under the umbrella term ‘hiccup sequences’ with a direct skeletal influence from a ‘remarkable’ paper by Dekking, Bosma, and Steiner (2018) describing one such sequence in five very interesting ways. In this talk, we begin with one such way that uses morphisms. Using the Dumont-Thomas numeration system (DTNS) associated with the morphism, we prove a Kimberling’s conjecture on the OEIS about the bounds of a difference sequence related to one such sequence. There is also some use of Walnut software for Ollinger provides a tool that converts the DTNS into a set of Walnut-readable automata.

dynamical systemsnumber theory

Audience: researchers in the topic

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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