Dynamical Systems seminar - Monochromatic Arithmetic Progressions in the Fibonacci word

Dates

Wednesday, February 7, 2024 - 13:30 to 14:30

Speaker: Gandhar Joshi (The Open University)

Abstract: We study monochromatic arithmetic progressions (MAPs) in automatic sequences. This was initially inspired by Van der Waerden’s celebrated theorem in Ramsay theory. Nagai et al. (2021) proved that MAPs in a particular class of constant-length substitution fixed points are never infinite. We study the MAPs in non-constant length substitutions and prove that MAPs in the Fibonacci word are never infinite, as well as a few interesting numerical results using 'Walnut'.