Moscow Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Moscow Mathematical Journal, 2003, Volume 3, Number 2, Pages 647–659
DOI: https://doi.org/10.17323/1609-4514-2003-3-2-647-659 (Mi mmj103) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Counting real rational functions with all real critical values

B. Z. Shapiroa, A. D. Vainshteinb

a Stockholm University
b University of Haifa
Full-text PDF Citations (7)
References:
PDF
HTML
DOI: https://doi.org/10.17323/1609-4514-2003-3-2-647-659
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.
Received: August 5, 2002
Bibliographic databases:
MSC: 14N10; 14Pxx; 26C15
Language: English
Citation: B. Z. Shapiro, A. D. Vainshtein, “Counting real rational functions with all real critical values”, Mosc. Math. J., 3:2 (2003), 647–659
Citation in format AMSBIB
\Bibitem{ShaVai03}
\by B.~Z.~Shapiro, A.~D.~Vainshtein
\paper Counting real rational functions with all real critical values
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 647--659
\mathnet{http://mi.mathnet.ru/mmj103}
\crossref{https://doi.org/10.17323/1609-4514-2003-3-2-647-659}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2025277}
\zmath{https://zbmath.org/?q=an:1039.58035}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000208594200016}
\elib{https://elibrary.ru/item.asp?id=8379118}
Linking options:
  • https://www.mathnet.ru/eng/mmj103
  • https://www.mathnet.ru/eng/mmj/v3/i2/p647
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Moscow Mathematical Journal
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024