A bias parity slope on the simplest non-periodic binary words. (April 2023)

• Record Type: Journal Article
• Authors: Cobeli, Cristian; Zaharescu, Alexandru
• Is Part Of: Chaos, solitons and fractals. Volume 169(2023)
• Publication Date: 2023-04
• Subjects: primary 11B99 -- secondary 11M41 05A05 68R15; Sturmian words -- Complexity of words -- Dirichlet series; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2023.113257
• Languages: English
• ISSNs: 0960-0779

Abstract

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