- FindStat

Identifier

Mp00224: Binary words —runsort⟶ Binary words
St001417: Binary words ⟶ ℤ

Values

0 => 0 => 1

1 => 1 => 1

00 => 00 => 2

01 => 01 => 1

10 => 01 => 1

11 => 11 => 2

000 => 000 => 3

001 => 001 => 2

010 => 001 => 2

011 => 011 => 2

100 => 001 => 2

101 => 011 => 2

110 => 011 => 2

111 => 111 => 3

0000 => 0000 => 4

0001 => 0001 => 3

0010 => 0001 => 3

0011 => 0011 => 2

0100 => 0001 => 3

0101 => 0101 => 3

0110 => 0011 => 2

0111 => 0111 => 3

1000 => 0001 => 3

1001 => 0011 => 2

1010 => 0011 => 2

1011 => 0111 => 3

1100 => 0011 => 2

1101 => 0111 => 3

1110 => 0111 => 3

1111 => 1111 => 4

00000 => 00000 => 5

00001 => 00001 => 4

00010 => 00001 => 4

00011 => 00011 => 3

00100 => 00001 => 4

00101 => 00101 => 3

00110 => 00011 => 3

00111 => 00111 => 3

01000 => 00001 => 4

01001 => 00101 => 3

01010 => 00101 => 3

01011 => 01011 => 3

01100 => 00011 => 3

01101 => 01011 => 3

01110 => 00111 => 3

01111 => 01111 => 4

10000 => 00001 => 4

10001 => 00011 => 3

10010 => 00011 => 3

10011 => 00111 => 3

10100 => 00011 => 3

10101 => 01011 => 3

10110 => 00111 => 3

10111 => 01111 => 4

11000 => 00011 => 3

11001 => 00111 => 3

11010 => 00111 => 3

11011 => 01111 => 4

11100 => 00111 => 3

11101 => 01111 => 4

11110 => 01111 => 4

11111 => 11111 => 5

000000 => 000000 => 6

000001 => 000001 => 5

000010 => 000001 => 5

000011 => 000011 => 4

000100 => 000001 => 5

000101 => 000101 => 4

000110 => 000011 => 4

000111 => 000111 => 3

001000 => 000001 => 5

001001 => 001001 => 5

001010 => 000101 => 4

001011 => 001011 => 3

001100 => 000011 => 4

001101 => 001101 => 4

001110 => 000111 => 3

001111 => 001111 => 4

010000 => 000001 => 5

010001 => 000101 => 4

010010 => 000101 => 4

010011 => 001101 => 4

010100 => 000101 => 4

010101 => 010101 => 5

010110 => 001011 => 3

010111 => 010111 => 4

011000 => 000011 => 4

011001 => 001011 => 3

011010 => 001011 => 3

011011 => 011011 => 5

011100 => 000111 => 3

011101 => 010111 => 4

011110 => 001111 => 4

011111 => 011111 => 5

100000 => 000001 => 5

100001 => 000011 => 4

100010 => 000011 => 4

100011 => 000111 => 3

100100 => 000011 => 4

100101 => 001011 => 3

100110 => 000111 => 3

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Description

The length of a longest palindromic subword of a binary word.
A subword of a word is a word obtained by deleting letters. This statistic records the maximal length of a palindromic subword.
Any binary word of length $n$ contains a palindromic subword of length at least $n/2$, obtained by removing all occurrences of the letter which occurs less often. This bound is obtained by the word beginning with $n/2$ zeros and ending with $n/2$ ones.

Map

runsort

Description

The word obtained by sorting the weakly increasing runs lexicographically.