RowOfLargestEntry

The row containing the largest entry.

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RowOfLargestEntry(tableau)The row containing the largest entry.

Typed signatures

Type	Package	Applies
(standard_tableau) -> number	combinatorics	always

Domain: Tableau statistics

Details

• Defined over StandardTableau as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a StandardTableau and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
• The empty tableau, which has no such entry, gives 0.

Definition

Epsil, as the implementation runs it.

on StandardTableau, over _x

0 if Length(_x) < 1 else Apply(
                                (lasts: list<integer>) => IndexOf(
                                                                   lasts,
                                                                   Max(lasts),
                                                                 ),
                                Map(Function(Last(r), r), _x),
                              )

Examples

Basic #

the standard tableau $[[1,2,4],[3,6],[5]]$

live ↗

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

Properties #

FindStat's value for [[1]]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{StandardTableau}}([[1]]), \text{RowOfLargestEntry})$Out$1$

Known value · FindStat St000733

FindStat's value for [[1,2]]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{StandardTableau}}([[1, 2]]), \text{RowOfLargestEntry})$Out$1$

Known value · FindStat St000733

FindStat's value for [[1,2,3]]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{StandardTableau}}([[1, 2, 3]]), \text{RowOfLargestEntry})$Out$1$

Known value · FindStat St000733

About

Examples	4
Crosswalk	FindStat