Abstract
There is a 1-1-correspondence between isomorphism classes of finite dimensional vector lattices and finite rooted unlabelled trees. Thus the problem of counting isomorphism classes of finite dimensional vector lattices reduces to the well-known combinatorial problem of counting these trees. The correspondence is used to identify the class of congruence lattices of finite-dimensional vector lattices as the class of finite dual relative Stone algebras, in partial answer to a question posed by Birkhoff.
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