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On Tamari lattices. (English) Zbl 0811.06005

The Tamari lattice \(T_ n\) is defined as the set of all binary bracketings on \(n+1\) symbols ordered by applying the associative rule only in one direction. Using a vector representation it is proved that this order defines a lattice. To determine the structure of Tamari lattices, the author uses methods of formal concept analysis. The Tamari lattices are bounded subdirectly irreducible lattices. A construction method for these lattices is given. Tamari lattices and their congruence lattices have the same number of elements.

MSC:

06B05 Structure theory of lattices
06B10 Lattice ideals, congruence relations

Citations:

Zbl 0778.06007
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References:

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