PrefixSumProduct

The product of the prefix sums p(1) + ... + p(i) for i < n.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001482via Permutation✓↗

PrefixSumProduct(p)The product of the prefix sums p(1) + ... + p(i) for i < n.

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

1 if Length(_x) < 2 else Product(Map(
                                      Function(Sum(Map(
                                                        Function(_x[j], j),
                                                        Range(1, i),
                                                      )), i),
                                      Range(1, Length(_x) - 1, 1),
                                    ))

Examples

Basic #

the one-line word $312$

live ↗

In$\mathrm{PrefixSumProduct}({\operatorname{Permutation}}([3, 1, 2]))$Out$12$

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

live ↗

In$\mathrm{PrefixSumProduct}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$12$

the one-line word $2413$

live ↗

In$\mathrm{PrefixSumProduct}({\operatorname{Permutation}}([2, 4, 1, 3]))$Out$84$

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001482

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St001482

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St001482

About

Examples	6
Crosswalk	FindStat