nLab Motzkin number

Contents

Context

Combinatorics

combinatorics

enumerative combinatorics

graph theory

rewriting

Polytopes

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category: combinatorics

Contents

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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)

References

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