MotzkinAlgebra

: the planar diagrams whose blocks have size at most two — so points may also be left unpaired. Dimension , the Motzkin numbers.

WikipediaMotzkin numberMathWorldMotzkinNumberWikidataQ2915234DLMF26.6.E2OEISA001006

MotzkinAlgebra(n)the Motzkin algebra on strands

RookAlgebra(n)partial permutations — blocks of size ≤ 2, each pairing a top with a bottom

SymmetricGroupAlgebra(n)permutation diagrams only — dimension

Domain: Diagram algebras

Details

Dimension = 2, 9, 51, 323 — the Motzkin numbers, which count the same paths with a flat step that Catalan counts without
Contains TemperleyLiebAlgebra: dropping the requirement that every point be paired is exactly what turns Catalan into Motzkin
`RookAlgebra(n)` counts — the partial permutations, i.e. the placements of non-attacking rooks
`SymmetricGroupAlgebra(n)` is the group algebra of , the diagrams that are honest bijections

Examples

See also: TemperleyLiebAlgebra, PartitionAlgebra, Diagram