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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Dedicated to the memory of Alan Day
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Hobart, M.F., Smith, J.D.H. Vector lattices and rooted trees. Algebra Universalis 34, 110–117 (1995). https://doi.org/10.1007/BF01200493
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DOI: https://doi.org/10.1007/BF01200493