A bias parity question for Sturmian words

Abstract

We analyze a natural parity problem on the divisors associated to Sturmian words. We find a clear bias towards the odd divisors and obtain a sharp asymptotic estimate for the average of the difference odd-even function tamed by a mollifier, which proves various experimental results.

12 pages and 10 figures

References in corpus (3)

• Quasiperiodic infinite words : multi-scale case and dynamical properties
• On the Farey fractions with denominators in arithmetic progression
• The distribution of rationals in residue classes