Meanders were introduced by Dergachev and A. Kirillov as planar representations of biparabolic (seaweed) subalgebras of sl(n). We find that each meander can be identified with a deterministic sequence of graph- theoretic moves, which we call the meanders signature. Using the signature we develop a fast algorithm for the computation of the index of a Lie algebra associated with the meander. And using a sensitive refinement of this signature, we are able to prove an important conjecture of Gerstenhaber and Giaquinto which asserts that the spectrum of the adjoint of a principal element in a Frobenius (index zero) seaweed Lie algebra consists of an unbroken sequence of integers.

We advance this line of study by considering the symplectic case.