Polynomial equations with one catalytic variable, algebraic series, and map enumeration

Mireille Bousquet-Mélou, Arnaud Jehanne

Let $F(t,u)\equiv F(u)$ be a formal power series in $t$ with polynomial coefficients in $u$. Let $F\_1,...,F\_k$ be $k$ formal power series in $t$, independent of $u$. Assume all…