Geodesic
The Local Rank of an Ergodic Symmetric Power $T^{\odot n}$ Does Not Exceed $n!\,n^{-n}$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 92-96

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The infinity of the rank of ergodic symmetric powers of automorphisms of the Lebesgue space is proved, and sharp upper bounds for their local rank are found.
Mots-clés : ergodic transformation
Keywords: local rank, symmetric tensor product. 
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     title = {The {Local} {Rank} of an {Ergodic} {Symmetric} {Power} $T^{\odot n}$ {Does} {Not} {Exceed} $n!\,n^{-n}$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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V. V. Ryzhikov. The Local Rank of an Ergodic Symmetric Power $T^{\odot n}$ Does Not Exceed $n!\,n^{-n}$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 92-96. http://geodesic.mathdoc.fr/item/FAA_2013_47_1_a10/