Geodesic
Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms $T$ and $T^{-1}$
Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 889-895

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It is shown that an automorphism of a Lebesgue space may admit a partial multiple mixing on subsequences of the form $\{h_n\}$ and $\{3h_n\}$ even when its inverse does not have this property. 
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     author = {V. V. Ryzhikov},
     title = {Partial {Multiple} {Mixing} on {Subsequences} {May} {Distinguish} between {Automorphisms} $T$ and $T^{-1}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {889--895},
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     volume = {74},
     number = {6},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a8/}
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V. V. Ryzhikov. Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms $T$ and $T^{-1}$. Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 889-895. http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a8/