Enumeration of walks on lattices. I

Details Enumeration of walks on lattices. I Enumeration of walks on lattices. I

1998-03-26

arxiv.org/abs/math/9803128v1

Mathematics

Combinatorics

37 pages, see also http://www.math.upenn.edu/~mihailov/papers.html

Scientific paper

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.

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