Dichromatic sum equations for outerplanar maps (Q1309141)

The purpose of the present paper is to provide a functional equation satisfied by the dichromatic sum function of non-separable outerplanar maps. The main result is the following theorem: The functional equation of \(\psi=\psi(x,y,z;\mu,\nu)\) with \(\psi^*=\psi(x,y,1)\) as unknown as \[ \psi= xyz\left(\nu z+\mu y+{\psi xyz^ 2\over y+\nu xy-\psi^*} + {\delta_ z\psi\over 1-\nu xz}\right) \] is well defined on the domain of all power series with polynomials of \(\mu\) and \(\nu\) as coefficients of the undeterminates \(x\), \(y\), \(z\).