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| In this talk we discuss the relationship between permutation entropy and Kolmogorov-Sinai entropy.
The considerations are based on comparing two special partitions of the state space induced by ordinal patterns.
An ordinal pattern of order $d$ describes the order relations between the components of a $(d+1)$-dimensional vector.
We consider, on the one hand, the partition ${\cal P}(d+n-1)$ provided by ordinal patterns of order $d+n-1$
and, on the other hand, the partition ${\cal P}(d)_n$ provided by $n$ successive ordinal patterns of order $d$.
Due to recent results, the answer to the question of how much more information longer ordinal patterns of order $d+n-1$ provide than $n$ successive shorter ordinal patterns of order $d$ gives an approach to comparing the entropies.
We present some extreme examples shedding some new light on the problem of coincidence of the entropies.
We also discuss some combinatorial properties regarding the partitions ${\cal P}(d+n-1)$ and ${\cal P}(d)_n$,
which provide a better understanding of the considered problem. |
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