PrimeColumnSums

Positions i with i + p(i) prime.

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PrimeColumnSums(p)Positions i with i + p(i) prime.

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 Count(Filter(
                                       Range(1, Length(_x)),
                                       Function(i + _x[i] >= 2 && Count(Filter(
                                                                                Range(2, i + _x[i]),
                                                                                Function(d <
                                                                                         i + _x[i] &&
                                                                                         (i + _x[i]) %
                                                                                         d ==
                                                                                         0, d),
                                                                              )) ==
                                                                  0, i),
                                     ))

Examples

Basic #

the one-line word $312$

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001285

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St001285

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St001285

About

Examples	5
Crosswalk	FindStat