LongestPalindromicPrefix

The length of the longest prefix that reads the same backwards.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001415via BinaryWord✓↗

LongestPalindromicPrefix(word)The length of the longest prefix that reads the same backwards.

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 St001415.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

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

Examples

Basic #

the word $110100111$

live ↗

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

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St001415

FindStat's value for 1

live ↗

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

Known value · FindStat St001415

FindStat's value for 00

live ↗

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

Known value · FindStat St001415

About

Examples	4
Crosswalk	FindStat