nLab Motzkin number

Idea

(…)

Definition

(….)

Properties

Relation to standard Young tableaux

The $n$th Motzkin number equals the the number $\left\vert sYT_n(3) \right\vert$ of standard Young tableaux with $n$ boxes and $\leq 3$ rows.

(Regev 81)

Related concepts

• Catalan number

• chord diagram

References

See also

• Wikipedia, Motzkin number

As counting standard Young tableaux with $\leq 3$ rows:

• Amitai Regev, Asymptotic values for degrees associated with strips of young diagrams, Advances in Mathematics Volume 41, Issue 2, August 1981, Pages 115-136 (doi:10.1016/0001-8708(81)90012-8)