ReverseComplementFactorHalfLengthStartingWithOne

Half the length of the longest factor that is its own reverse complement and begins with a 1.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001421via BinaryWord✓↗

ReverseComplementFactorHalfLengthStartingWithOne(word)Half the length of the longest factor that is its own reverse complement and begins with a 1.

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 St001421.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

0 if Length(_x) < 2 else Max(Join(
                                   [0],
                                   Map(
                                        Function(h * Max(Map(
                                                              Function(
                                                                        1 if _x[i] ==
                                                                             1 &&
                                                                             Max(Sum(Map(
                                                                                          Function(1 if _x[i +
                                                                                                           (m - 1)] +
                                                                                                        _x[i +
                                                                                                           (2h - m)] ==
                                                                                                        1 else 0, m),
                                                                                          Range(1, h, 1),
                                                                                        )), 0) ==
                                                                             h else 0,
                                                                        i,
                                                                      ),
                                                              Range(
                                                                     1,
                                                                     Length(_x) -
                                                                     2h + 1,
                                                                     1,
                                                                   ),
                                                            )), h),
                                        Range(1, (Length(_x) - Length(_x) % 2) /
                                                 2, 1),
                                      ),
                                 ))

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{ReverseComplementFactorHalfLengthStartingWithOne}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$3$

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St001421

FindStat's value for 1

live ↗

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

Known value · FindStat St001421

FindStat's value for 00

live ↗

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

Known value · FindStat St001421

About

Examples	4
Crosswalk	FindStat