Factor-balancedness, linear recurrence and factor complexity
Pierre POPOLI
Université de Waterloo (Ontario, Canada)
https://sites.google.com/view/pierre-popoli-en
Date(s) : 13/03/2026 iCal
11h00 - 12h00
In the study of infinite words, various notions of balancedness provide quantitative measures for how regularly letters or factors occur, and they find applications in several areas of mathematics and theoretical computer science. In this talk, I will present new results about factor-balancedness and uniform factor-balancedness. First, we establish general sufficient conditions for an infinite word to be (uniformly) factor-balanced, applicable in particular to any given linearly recurrent word. These conditions are formulated in terms of $\mathcal{S}$-adic representations and generalize results of Adamczewski on primitive substitutive words. Also, as an application of our criteria, we characterize the Sturmian words and ternary Arnoux–Rauzy words that are uniformly factor-balanced as precisely those with bounded weak partial quotients. If time permits, I will also explain the construction of our example of a factor-balanced word with exponential factor complexity, inspired by a question raised in 2025 by Arnoux, Berthé, Minervino, Steiner, and Thuswaldner.
This talk is based on joint work with B. Espinoza and M. Stipulanti.
Emplacement
Saint-Charles - FRUMAM (2ème étage)
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