BaselineCrossings

The times the path, a 1 a step up and a 0 a step down, crosses the baseline.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001730via BinaryWord✓↗

BaselineCrossings(word)The times the path, a 1 a step up and a 0 a step down, crosses the baseline.

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.
• FindStat's St001730.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

0 if Length(_x) < 2 else Apply(
                                (h: list<integer>) => Max(Sum(Map(
                                                                   Function(1 if _x[i] ==
                                                                                 _x[i + 1] &&
                                                                                 h[i - 1 +
                                                                                   1] ==
                                                                                 1 -
                                                                                 2 * _x[i] else 0, i),
                                                                   Range(
                                                                          1,
                                                                          Length(_x) -
                                                                          1,
                                                                        ),
                                                                 )), 0),
                                Apply((a_init: list<integer>) => Fold(
                                                                       (
                                                                         a: list<integer>,
                                                                         b,
                                                                       ) => Apply(
                                                                                  (a_next: list<integer>) => a_next,
                                                                                  Join(a, [a[Length(a)] +
                                                                                           (2 * _x[b] -
                                                                                            1)]),
                                                                                ),
                                                                       a_init,
                                                                       Range(1, Length(_x)),
                                                                     ), [0]),
                              )

Examples

Basic #

the word $110100111$

live ↗

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

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St001730

FindStat's value for 1

live ↗

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

Known value · FindStat St001730

FindStat's value for 00

live ↗

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

Known value · FindStat St001730

About

Examples	4
Crosswalk	FindStat