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.
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页码：647 / 659
页数：13
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