- FindStat

Identifier

Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000983: Binary words ⟶ ℤ

Values

[1,0] => 10 => 01 => 2
[1,0,1,0] => 1010 => 0101 => 4
[1,1,0,0] => 1100 => 0011 => 2
[1,0,1,0,1,0] => 101010 => 010101 => 6
[1,0,1,1,0,0] => 101100 => 001101 => 3
[1,1,0,0,1,0] => 110010 => 010011 => 3
[1,1,0,1,0,0] => 110100 => 001011 => 4
[1,1,1,0,0,0] => 111000 => 000111 => 2
[1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 8
[1,0,1,0,1,1,0,0] => 10101100 => 00110101 => 5
[1,0,1,1,0,0,1,0] => 10110010 => 01001101 => 3
[1,0,1,1,0,1,0,0] => 10110100 => 00101101 => 4
[1,0,1,1,1,0,0,0] => 10111000 => 00011101 => 3
[1,1,0,0,1,0,1,0] => 11001010 => 01010011 => 5
[1,1,0,0,1,1,0,0] => 11001100 => 00110011 => 2
[1,1,0,1,0,0,1,0] => 11010010 => 01001011 => 4
[1,1,0,1,0,1,0,0] => 11010100 => 00101011 => 6
[1,1,0,1,1,0,0,0] => 11011000 => 00011011 => 3
[1,1,1,0,0,0,1,0] => 11100010 => 01000111 => 3
[1,1,1,0,0,1,0,0] => 11100100 => 00100111 => 3
[1,1,1,0,1,0,0,0] => 11101000 => 00010111 => 4
[1,1,1,1,0,0,0,0] => 11110000 => 00001111 => 2
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0001110101 => 5
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0010101101 => 6
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0001101101 => 3
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0010011101 => 3
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0001011101 => 4
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0000111101 => 3
[1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0001110011 => 2
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 0010101011 => 8
[1,1,0,1,0,1,1,0,0,0] => 1101011000 => 0001101011 => 5
[1,1,0,1,1,0,0,1,0,0] => 1101100100 => 0010011011 => 3
[1,1,0,1,1,0,1,0,0,0] => 1101101000 => 0001011011 => 4
[1,1,0,1,1,1,0,0,0,0] => 1101110000 => 0000111011 => 3
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 0010100111 => 5
[1,1,1,0,0,1,1,0,0,0] => 1110011000 => 0001100111 => 2
[1,1,1,0,1,0,0,1,0,0] => 1110100100 => 0010010111 => 4
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 0001010111 => 6
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 0000110111 => 3
[1,1,1,1,0,0,0,1,0,0] => 1111000100 => 0010001111 => 3
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 0001001111 => 3
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 0000101111 => 4
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0000011111 => 2

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$F_{1} = q^{2}$

$F_{2} = q^{2} + q^{4}$

$F_{3} = q^{2} + 2\ q^{3} + q^{4} + q^{6}$

$F_{4} = 2\ q^{2} + 5\ q^{3} + 3\ q^{4} + 2\ q^{5} + q^{6} + q^{8}$

Description

The length of the longest alternating subword.
This is the length of the longest consecutive subword of the form

$010...$ or of the form

$101...$ .

Map

reverse

Description

Return the reversal of a binary word.

Map

to binary word

Description

Return the Dyck word as binary word.