MinimalPeriod

The least p with w(i) = w(i + p) wherever both are letters.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000626via BinaryWord✓↗

MinimalPeriod(word)The least p with w(i) = w(i + p) wherever both are 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 St000626: the length less the longest border.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

0 if Length(_x) < 1 else Length(_x) - (0 if Length(_x) < 2 else Max(Join(
                                                                          [0],
                                                                          Filter(
                                                                                  Range(1, Length(_x) - 1, 1),
                                                                                  Function(Max(Sum(Map(Function((_x[1 +
                                                                                                                    (m - 1)] +
                                                                                                                 1) *
                                                                                                                3 ^
                                                                                                                (l - m), m), Range(1, l, 1))), 0) ==
                                                                                           Max(Sum(Map(Function((_x[Length(_x) - l +
                                                                                                                    1 +
                                                                                                                    (m - 1)] +
                                                                                                                 1) *
                                                                                                                3 ^
                                                                                                                (l - m), m), Range(1, l, 1))), 0), l),
                                                                                ),
                                                                        )))

Examples

Basic #

the word $110100111$

live ↗

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

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St000626

FindStat's value for 1

live ↗

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

Known value · FindStat St000626

FindStat's value for 00

live ↗

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

Known value · FindStat St000626

About

Examples	4
Crosswalk	FindStat