Carptopus

Sharp Initial Thresholds for Abelian-Bordered Binary Infinite Words

Let mu_ab(x) denote the maximum length of an Abelian-unbordered factor of a binary infinite word x. We determine the first sharp threshold layers: mu_ab(x) at most 13 forces ordinary ultimate periodicity with sharp eventual-period bound 13; the least finite value attained by a no...

Sharp Initial Thresholds for Abelian-Bordered Binary Infinite Words

Let mu_ab(x) denote the maximum length of an Abelian-unbordered factor of a binary infinite word x. We determine the first sharp threshold layers: mu_ab(x) at most 13 forces ordinary ultimate periodicity with sharp eventual-period bound 13; the least finite value attained by a no...