MaximalModularDisplacement

The largest cyclic distance between p(i) and i, taken mod n.

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MaximalModularDisplacement(p)The largest cyclic distance between p(i) and i, taken mod n.

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(Min([(_x[i] - i + Length(_x)) %
                                               Length(_x), (i - _x[i] + Length(_x)) %
                                                 Length(_x)]), i), Range(1, Length(_x))))

Examples

Basic #

the one-line word $312$

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1,2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2]), \text{MaximalModularDisplacement})$Out$0$

Known value · FindStat St001569

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St001569

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

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2, 3]), \text{MaximalModularDisplacement})$Out$0$

Known value · FindStat St001569

About

Examples	5
Crosswalk	FindStat