FirstEntryInLastRow

The first entry in the last row.

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FirstEntryInLastRow(tableau)The first entry in the last row.

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((reading: list<integer>) => Apply(
                                                                  (lengths: list<integer>) => reading[Length(reading) - lengths[Length(_x)] +
                                                                                                      1],
                                                                  Map(
                                                                       Function(Length(r), r),
                                                                       _x,
                                                                     ),
                                                                ), Flatten(_x))

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [[1]]

live ↗

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

Known value · FindStat St000738

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

live ↗

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

Known value · FindStat St000738

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

live ↗

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

Known value · FindStat St000738

About

Examples	4
Crosswalk	FindStat