StrictlyIncreasingRuns

The maximal runs of strictly increasing letters.

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StrictlyIncreasingRuns(word)The maximal runs of strictly increasing letters.

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 St000393: one more than the weak descents.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

0 if Length(_x) < 1 else 1 + (0 if Length(_x) < 2 else Count(Filter(
                                                                     Range(
                                                                            1,
                                                                            Length(_x) -
                                                                            1,
                                                                          ),
                                                                     Function(_x[i] >=
                                                                              _x[i + 1], i),
                                                                   )))

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{StrictlyIncreasingRuns}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$7$

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St000393

FindStat's value for 1

live ↗

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

Known value · FindStat St000393

FindStat's value for 00

live ↗

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

Known value · FindStat St000393

About

Examples	4
Crosswalk	FindStat