Combinatorics of Seaweed Meanders

We show that the index of a uniformly random seaweed meander satisfies a central limit theorem and is asymptotically equidistributed with respect to any modulus. We also extend work by Archer, Geary, and Laudone on the enumeration of seaweed meanders whose compositions have restricted parts. Finally, we give a connection to billiards in triangular shapes, which is related to a result of Eu, Fu, and Hsu.