OddOneRunCount

The number of maximal runs of ones of odd length.

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OddOneRunCount(word)The number of maximal runs of ones of odd length.

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] + (1 - b) * (a[1] % 2)], a, b),
      [0, 0],
      Join(_x, [0]),
    )[2]

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{OddOneRunCount}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$2$

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St000389

FindStat's value for 1

live ↗

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

Known value · FindStat St000389

FindStat's value for 00

live ↗

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

Known value · FindStat St000389

About

Examples	4
Crosswalk	FindStat