PartitionAlgebra

: every set partition of points. The largest of the family — all the others are subalgebras cut out by admitting fewer diagrams. Dimension , the Bell numbers.

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PartitionAlgebra(n)the partition algebra on strands

PlanarPartitionAlgebra(n)only the planar diagrams — dimension

Domain: Diagram algebras

Details

• Dimension : 2, 15, 203, 4140 for — the Bell numbers at even index
• Restricting to planar diagrams gives , the Catalan numbers
• Basis lists the diagrams and AlgebraDimension answers from the closed form, so the dimension is available well past the point where listing is useful
• Element tests membership, which is what makes the inclusions checkable

Examples

See also: Diagram, BrauerAlgebra, TemperleyLiebAlgebra