  This work develops a methodical approach to counting of walks on cartesian
products, biproducts, symmetric and exterior powers and bipowers, Schur
operations, coverings and semicoverings of weighted graphs. For weight and root
lattices of semisimple Lie algebras, this approach allows us to compute various
combinatorial and representation-theoretical constants, in particular, the
number of plane symplectic wave graphs with given number of vertices.
