The present paper is devoted to the combinatorial descriptions of the connected components of certain open sets of the space of real or complex polynomials of a fixed degree. One instance is the open set of generic real polynomials (i.e. with distinct critical values). Describing the connected components of the open set of real lemniscate generic polynomials (i.e. with critical values with distinct non-zero absolute values), we give in particular a geometric proof of the equality between the number of connected components of the space $\mathcal {L}_n$ of complex lemniscate generic polynomials of degree $n+1$ and the number of connected components of the space of real monic polynomials of degree $n + 1$ with $n$ distinct real critical values, the lemniscate configurations occurring from real polynomials.