OccurrencesOf41352Or42351Or51342Or52341

Quintuples ordered as 41352, 42351, 51342 or 52341.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001059via Permutation✓↗

OccurrencesOf41352Or42351Or51342Or52341(p)Quintuples ordered as 41352, 42351, 51342 or 52341.

Typed signatures

Type	Package	Applies
(list<integer> | 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 also a bare list of integers: this reading compares entries with each other rather than with their positions, so it stands on any sequence.

Definition

Epsil, as the implementation runs it.

on Permutation, over _x

0 if Length(_x) < 5 else Sum(Map(
                                  Function(Sum(Map(Function(Sum(Map(
                                                                     Function(Sum(Map(
                                                                                       Function(Count(Filter(
                                                                                                              Range(l + 1, Length(_x)),
                                                                                                              Function(_x[j] < _x[m] &&
                                                                                                                       _x[m] < _x[k] &&
                                                                                                                       _x[k] < _x[i] &&
                                                                                                                       _x[i] < _x[l] ||
                                                                                                                       _x[m] < _x[j] &&
                                                                                                                       _x[j] < _x[k] &&
                                                                                                                       _x[k] < _x[i] &&
                                                                                                                       _x[i] < _x[l] ||
                                                                                                                       _x[j] < _x[m] &&
                                                                                                                       _x[m] < _x[k] &&
                                                                                                                       _x[k] < _x[l] &&
                                                                                                                       _x[l] < _x[i] ||
                                                                                                                       _x[m] < _x[j] &&
                                                                                                                       _x[j] < _x[k] &&
                                                                                                                       _x[k] < _x[l] &&
                                                                                                                       _x[l] < _x[i], m),
                                                                                                            )), l),
                                                                                       Range(k + 1, Length(_x) - 1),
                                                                                     )), k),
                                                                     Range(
                                                                            j +
                                                                            1,
                                                                            Length(_x) -
                                                                            2,
                                                                          ),
                                                                   )), j), Range(
                                                                                 i + 1,
                                                                                 Length(_x) - 3,
                                                                               ))), i),
                                  Range(1, Length(_x) - 4),
                                ))

Examples

Basic #

the one-line word $312$

live ↗

In$\mathrm{OccurrencesOf41352Or42351Or51342Or52341}({\operatorname{Permutation}}([3, 1, 2]))$Out$0$

the one-line word $312$, as a plain list

live ↗

In$\mathrm{OccurrencesOf41352Or42351Or51342Or52341}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$0$

the one-line word $2413$

live ↗

In$\mathrm{OccurrencesOf41352Or42351Or51342Or52341}({\operatorname{Permutation}}([2, 4, 1, 3]))$Out$0$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1]), \text{OccurrencesOf41352Or42351Or51342Or52341})$Out$0$

Known value · FindStat St001059

FindStat's value for [1,2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2]), \text{OccurrencesOf41352Or42351Or51342Or52341})$Out$0$

Known value · FindStat St001059

FindStat's value for [2,1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([2, 1]), \text{OccurrencesOf41352Or42351Or51342Or52341})$Out$0$

Known value · FindStat St001059

About

Examples	6
Crosswalk	FindStat