FirstOnePositionAfterAppendedOne

The position of the first 1 once a 1 is appended to the word: one more than the leading zeros.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000326via BinaryWord✓↗

FirstOnePositionAfterAppendedOne(word)The position of the first 1 once a 1 is appended to the word: one more than the leading zeros.

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

Fold(Function([a[1] * (1 - b), a[2] + a[1] * (1 - b)], a, b), [1, 0], _x)[2] + 1

Examples

Basic #

the word $110100111$

live ↗

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

Properties #

FindStat's value for 0

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0]), \text{FirstOnePositionAfterAppendedOne})$Out$2$

Known value · FindStat St000326

FindStat's value for 1

live ↗

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

Known value · FindStat St000326

FindStat's value for 00

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0, 0]), \text{FirstOnePositionAfterAppendedOne})$Out$3$

Known value · FindStat St000326

About

Examples	4
Crosswalk	FindStat