A bias parity question for Sturmian words
Cristian Cobeli, Alexandru Zaharescu
TL;DR
This paper investigates a parity bias in divisors related to Sturmian words, revealing a tendency towards odd divisors and providing precise asymptotic estimates supported by experimental data.
Contribution
It introduces a novel parity problem in Sturmian words and offers a sharp asymptotic analysis of the odd-even divisor bias.
Findings
Clear bias towards odd divisors in Sturmian words
Asymptotic estimates for the average difference between odd and even divisors
Experimental results confirming theoretical predictions
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.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals · Authorship Attribution and Profiling