%0 Journal Article
%T On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
%A Pieter Roffelsen
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlev¨¦ equation. It has been conjectured that the number of real roots of the nth Yablonskii-Vorob'ev polynomial equals [(n+1)/2]. We prove this conjecture using an interlacing property between the roots of the Yablonskii-Vorob'ev polynomials. Furthermore we determine precisely the number of negative and the number of positive real roots of the nth Yablonskii-Vorob'ev polynomial.
%K second Painlev¨¦ equation
%K rational solutions
%K real roots
%K interlacing of roots
%K Yablonskii-Vorob'ev polynomials
%U http://dx.doi.org/10.3842/SIGMA.2012.099