FinalRises

The ascents at the end: n - 1 less the last descent position.

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FinalRises(p)The ascents at the end: n - 1 less the last descent position.

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) < 2 else Length(_x) - 1 -
                         (0 if Count(Filter(
                                             Range(1, Length(_x) - 1),
                                             Function(_x[i] > _x[i + 1], i),
                                           )) == 0 else Max(Filter(
                                                                   Range(
                                                                          1,
                                                                          Length(_x) -
                                                                          1,
                                                                        ),
                                                                   Function(_x[i] >
                                                                            _x[i +
                                                                               1], i),
                                                                 )))

Examples

Basic #

the one-line word $312$

live ↗

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

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

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St000989

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St000989

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

live ↗

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

Known value · FindStat St000989

About

Examples	6
Crosswalk	FindStat