  Rational solutions and special polynomials associated with the generalized
K_2 hierarchy are studied. This hierarchy is related to the Sawada-Kotera and
Kaup-Kupershmidt equations and some other integrable partial differential
equations including the Fordy-Gibbons equation. Differential-difference
relations and differential equations satisfied by the polynomials are derived.
The relationship between these special polynomials and stationary
configurations of point vortices with circulations Gamma and -2Gamma is
established. Properties of the polynomials are studied. Differential-difference
relations enabling one to construct these polynomials explicitly are derived.
Algebraic relations satisfied by the roots of the polynomials are found.
