MaximalDiagonalOccupancy

The most entries on one diagonal of the permutation matrix: the largest number of i sharing a p(i) - i.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000887via Permutation✓↗

MaximalDiagonalOccupancy(p)The most entries on one diagonal of the permutation matrix: the largest number of i sharing a p(i) - i.

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 Max(Map(
                                  Function(
                                            Count(Filter(
                                                          Range(1, Length(_x)),
                                                          Function(_x[j] - j ==
                                                                   _x[i] - i, j),
                                                        )),
                                            i,
                                          ),
                                  Range(1, Length(_x)),
                                ))

Examples

Basic #

the one-line word $312$

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St000887

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St000887

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

live ↗

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

Known value · FindStat St000887

About

Examples	5
Crosswalk	FindStat