Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$

V. V. Ryzhikov

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arXiv · 1108.5660

Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$

V. V. Ryzhikov

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Abstract

We prove that local rank of an ergodic symmetric power $T^{\odot n}$ does not exceed $n!n^{-n}$. A. Katok's old results show that this upper bound is exact. We prove also that $T^{\odot n}$ has infinite Rank as $n>1$.

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V. V. Ryzhikov. 2011-08-29. Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$. https://arxiv.org/abs/1108.5660

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