ReverseComplementFactorHalfLength

Half the length of the longest factor that is its own reverse complement.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001420via BinaryWord✓↗

ReverseComplementFactorHalfLength(word)Half the length of the longest factor that is its own reverse complement.

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 St001420. Such a factor has even length: its middle letter would be its own complement.

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 True &&
                                                                           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$\mathrm{ReverseComplementFactorHalfLength}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$3$

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St001420

FindStat's value for 1

live ↗

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

Known value · FindStat St001420

FindStat's value for 00

live ↗

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

Known value · FindStat St001420

About

Examples	4
Crosswalk	FindStat