Identifier
-
Mp00043:
Integer partitions
—to Dyck path⟶
Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00200: Binary words —twist⟶ Binary words
St000982: Binary words ⟶ ℤ
Values
[1] => [1,0,1,0] => 1010 => 0010 => 2
[2] => [1,1,0,0,1,0] => 110010 => 010010 => 2
[1,1] => [1,0,1,1,0,0] => 101100 => 001100 => 2
[3] => [1,1,1,0,0,0,1,0] => 11100010 => 01100010 => 3
[2,1] => [1,0,1,0,1,0] => 101010 => 001010 => 2
[1,1,1] => [1,0,1,1,1,0,0,0] => 10111000 => 00111000 => 3
[3,1] => [1,1,0,1,0,0,1,0] => 11010010 => 01010010 => 2
[2,2] => [1,1,0,0,1,1,0,0] => 11001100 => 01001100 => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => 10110100 => 00110100 => 2
[3,2] => [1,1,0,0,1,0,1,0] => 11001010 => 01001010 => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => 10110010 => 00110010 => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => 10101100 => 00101100 => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => 10101010 => 00101010 => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0010101100 => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0010101010 => 2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The length of the longest constant subword.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
twist
Description
Return the binary word with first letter inverted.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!