The Subword Complexity of a Two-Parameter Family of Sequences

We determine the subword complexity of the characteristic functions of a twoparameter family {An}∞n=1 of infinite sequences which are associated with the winning strategies for a family of 2-player games. A special case of the family has the form An = bnαc for all n ∈ Z>0, where α is a fixed positive irrational number. The characteristic functions of such sequences have been shown to have subword complexity n+1. We show that every sequence in the extended family has subword complexity O(n).