OnePositionSum

The sum of the positions of the ones.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000391via BinaryWord✓↗

OnePositionSum(word)The sum of the positions of the ones.

Typed signatures

Type	Package	Applies
(binary_word) -> number	combinatorics	always

Domain: Binary word statistics

Details

• Defined over BinaryWord as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a BinaryWord 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 BinaryWord, over _x

0 if Length(_x) < 1 else Max(Sum(Map(
                                      Function(_x[i] * i, i),
                                      Range(1, Length(_x)),
                                    )), 0)

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{OnePositionSum}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$31$

Properties #

FindStat's value for 0

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0]), \text{OnePositionSum})$Out$0$

Known value · FindStat St000391

FindStat's value for 1

live ↗

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

Known value · FindStat St000391

FindStat's value for 00

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0, 0]), \text{OnePositionSum})$Out$0$

Known value · FindStat St000391

About

Examples	4
Crosswalk	FindStat