This article is cited in 7 papers

Counting real rational functions with all real critical values

B. Z. Shapiro^a, A. D. Vainshtein<sup>b

a</sup> Stockholm University
^b University of Haifa

Abstract: We study the number $\#_n^\mathbb R$ of real rational degree $n$ functions (considered up to a linear fractional transformation of the independent variable) with a given set of $2n-2$ distinct real critical values. We present a combinatorial interpretation of these numbers and provide exact and asymptotic enumeration results for certain particular cases.

Key words and phrases: Real rational functions; real critical values; chord diagrams; enumeration.

MSC: 14N10; 14Pxx; 26C15

Received: August 5, 2002

Language: English

DOI: 10.17323/1609-4514-2003-3-2-647-659

Bibliographic databases:

• 
• 
• 
•