On the $k$-abelian complexity of the Cantor sequence

Jin Chen, Xiaotao Lü, Wen Wu

Published 2017-03-12Version 1

In this paper, we prove that for every integer $k \geq 1$, the $k$-abelian complexity function of the Cantor sequence $\mathbf{c} = 101000101\cdots$ is a $3$-regular sequence.