SymmetricBorderLength

The length of the longest prefix whose reverse is a suffix.

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SymmetricBorderLength(word)The length of the longest prefix whose reverse is a suffix.

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 St000296. The longest prefix that is a suffix read backwards is the run of leading positions i with w(i) = w(n + 1 - i).

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

0 if Length(_x) < 1 else Fold(
                               Function([
                                          a[1] * (1 if _x[b] == _x[Length(_x) +
                                                                   1 - b] else 0),
                                          a[2] + a[1] *
                                                 (1 if _x[b] == _x[Length(_x) +
                                                                   1 - b] else 0),
                                        ], a, b),
                               [1, 0],
                               Range(1, Length(_x)),
                             )[2]

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{SymmetricBorderLength}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$2$

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St000296

FindStat's value for 1

live ↗

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

Known value · FindStat St000296

FindStat's value for 00

live ↗

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

Known value · FindStat St000296

About

Examples	4
Crosswalk	FindStat