LongestPalindromicFactorStartingWithOne

The length of the longest palindromic factor that begins with a 1.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001419via BinaryWord✓↗

LongestPalindromicFactorStartingWithOne(word)The length of the longest palindromic factor that 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 St001419.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

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

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{LongestPalindromicFactorStartingWithOne}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$4$

Properties #

FindStat's value for 0

live ↗

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

Known value · FindStat St001419

FindStat's value for 1

live ↗

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

Known value · FindStat St001419

FindStat's value for 00

live ↗

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

Known value · FindStat St001419

About

Examples	4
Crosswalk	FindStat