EvenPalindromicPrefixHalfLength

Half the length of the longest palindromic prefix of even length.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001413via BinaryWord✓↗

EvenPalindromicPrefixHalfLength(word)Half the length of the longest palindromic prefix of even length.

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 St001413.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

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

Examples

Basic #

the word $110100111$

live ↗

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

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St001413

FindStat's value for 1

live ↗

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

Known value · FindStat St001413

FindStat's value for 00

live ↗

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

Known value · FindStat St001413

About

Examples	4
Crosswalk	FindStat