TwoRowTableau

The standard tableau of shape (n, n) with the positions of the up steps in its first row and of the down steps in its second.

FindStatMp00033via DyckPath↗

TwoRowTableau(DyckPath)The standard tableau of shape (n, n) with the positions of the up steps in its first row and of the down steps in its second.

Typed signatures

Type	Package	Applies
(dyck_path) -> standard_tableau	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a StandardTableau — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00033. Injective; the same tableau Promotion and InversePromotion act on.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{TwoRowTableau}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{StandardTableau}}([[1, 2, 5], [3, 4, 6]])$

About

Examples	1
Crosswalk	FindStat