Enumeration of walks on lattices. I

Aleksandrs Mihailovs
Department of Mathematics
University of Pennsylvania
Philadelphia, PA 19104-6395
http://www.math.upenn.edu/~mihailov/

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.  

Preprint (March 25, 1998)