LargestDirectSummandSize

The size of the largest block of p as a direct sum.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000844via Permutation✓↗

LargestDirectSummandSize(p)The size of the largest block of p as a direct sum.

Typed signatures

Type	Package	Applies
(permutation) -> number	combinatorics	always

Domain: Permutation statistics

Details

• Defined over Permutation as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a Permutation 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.

Definition

Epsil, as the implementation runs it.

on Permutation, over _x

0 if Length(_x) < 1 else Apply(
                                (b: list<integer>) => Max(Map(
                                                               Function(b[i + 1] -
                                                                        b[i], i),
                                                               Range(
                                                                      1,
                                                                      Length(b) -
                                                                      1,
                                                                      1,
                                                                    ),
                                                             )),
                                Join(
                                      [0],
                                      Filter(
                                              Range(1, Length(_x)),
                                              Function(Max(Map(
                                                                Function(
                                                                          _x[j],
                                                                          j,
                                                                        ),
                                                                Range(1, i),
                                                              )) == i, i),
                                            ),
                                    ),
                              )

Examples

Basic #

the one-line word $312$

live ↗

In$\mathrm{LargestDirectSummandSize}({\operatorname{Permutation}}([3, 1, 2]))$Out$3$

the one-line word $2413$

live ↗

In$\mathrm{LargestDirectSummandSize}({\operatorname{Permutation}}([2, 4, 1, 3]))$Out$4$

Properties #

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St000844

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St000844

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

live ↗

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

Known value · FindStat St000844

About

Examples	5
Crosswalk	FindStat