ProperBlocks

Windows p(i), ..., p(j) of two or more entries whose values are consecutive integers, the whole word excepted.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001160via Permutation✓↗

ProperBlocks(p)Windows p(i), ..., p(j) of two or more entries whose values are consecutive integers, the whole word excepted.

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) < 3 else Sum(Map(Function(Count(Filter(
                                                        Range(i + 1, Length(_x)),
                                                        Function(Max(Map(
                                                                          Function(_x[k], k),
                                                                          Range(i, j),
                                                                        )) -
                                                                 Min(Map(
                                                                          Function(_x[k], k),
                                                                          Range(i, j),
                                                                        )) == j - i, j),
                                                      )), i), Range(
                                                                    1,
                                                                    Length(_x) -
                                                                    1,
                                                                  ))) - 1

Examples

Basic #

the one-line word $312$

live ↗

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

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

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001160

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St001160

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St001160

About

Examples	6
Crosswalk	FindStat