An approach to comparing Kolmogorov-Sinai and permutation entropy

In this paper we discuss the relationship between permutation entropy and Kolmogorov-Sinai entropy in the one-dimensional case. For this, we consider partitions of the state space of a dynamical system using ordinal patterns of order (d + n- 1) on the one hand, and using n-letter words of ordinal patterns of order d on the other hand. The answer to the question of how different these partitions are provides an approach to comparing the entropies.