COUNTING REAL RATIONAL FUNCTIONS WITH ALL REAL CRITICAL VALUES

被引：6

作者：

Shapiro, Boris ^{[1
]}

Vainshtein, Alek ^{[2
,3
]}

机构：

[1] Univ Stockholm, Dept Math, S-10691 Stockholm, Sweden

[2] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

[3] Univ Haifa, Dept Comp Sci, IL-31905 Haifa, Israel

来源：

MOSCOW MATHEMATICAL JOURNAL | 2003年 / 3卷 / 02期

关键词：

Real rational functions; real critical values; chord diagrams; enumeration;

D O I：

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

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the number #(R)(n) 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.

引用

页码：647 / 659

页数：13

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