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Rational functions and Catalan numbers

Abstract : Set $C_n={2n\choose n}/(n+1)$ (the Catalan number). We show that there are $C_{n-1}$ possible topologically different cases for the disposition of the singular components of the level curves $|R|=$const, where $R=P/Q$ is a generic real rational function, deg$P=$deq$Q-1=n-1$ and the roots of $P$ and $Q$ are real, distinct and interlacing. All these $C_{n-1}$ cases are realizable by generic rational functions.
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https://hal.archives-ouvertes.fr/hal-00866113
Contributor : Vladimir Kostov <>
Submitted on : Thursday, September 26, 2013 - 8:54:53 AM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM

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  • HAL Id : hal-00866113, version 1

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Vladimir Kostov, Vladimir Kostov. Rational functions and Catalan numbers. Comptes Rendus de l'Academie des Sciences Bulgare, 2012, 65 (2), pp.147-152. ⟨hal-00866113⟩

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