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Counting real rational functions with all real critical values

B. Shapiro·A. Vainshtein
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Abstract

We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real critical values. We present a combinatorial reformulation of this number and pose several related questions.

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B. Shapiro, A. Vainshtein. 2002-09-06. Counting real rational functions with all real critical values. https://arxiv.org/abs/math/0209062

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