Identifier
Mp00095:
Integer partitions
—to binary word⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Images
[1] => 10 => [1,2] => [1,2]
[2] => 100 => [1,3] => [1,1,2]
[1,1] => 110 => [1,1,2] => [1,3]
[3] => 1000 => [1,4] => [1,1,1,2]
[2,1] => 1010 => [1,2,2] => [1,2,2]
[1,1,1] => 1110 => [1,1,1,2] => [1,4]
[4] => 10000 => [1,5] => [1,1,1,1,2]
[3,1] => 10010 => [1,3,2] => [1,2,1,2]
[2,2] => 1100 => [1,1,3] => [1,1,3]
[2,1,1] => 10110 => [1,2,1,2] => [1,3,2]
[1,1,1,1] => 11110 => [1,1,1,1,2] => [1,5]
[5] => 100000 => [1,6] => [1,1,1,1,1,2]
[4,1] => 100010 => [1,4,2] => [1,2,1,1,2]
[3,2] => 10100 => [1,2,3] => [1,1,2,2]
[3,1,1] => 100110 => [1,3,1,2] => [1,3,1,2]
[2,2,1] => 11010 => [1,1,2,2] => [1,2,3]
[2,1,1,1] => 101110 => [1,2,1,1,2] => [1,4,2]
[1,1,1,1,1] => 111110 => [1,1,1,1,1,2] => [1,6]
[6] => 1000000 => [1,7] => [1,1,1,1,1,1,2]
[5,1] => 1000010 => [1,5,2] => [1,2,1,1,1,2]
[4,2] => 100100 => [1,3,3] => [1,1,2,1,2]
[4,1,1] => 1000110 => [1,4,1,2] => [1,3,1,1,2]
[3,3] => 11000 => [1,1,4] => [1,1,1,3]
[3,2,1] => 101010 => [1,2,2,2] => [1,2,2,2]
[3,1,1,1] => 1001110 => [1,3,1,1,2] => [1,4,1,2]
[2,2,2] => 11100 => [1,1,1,3] => [1,1,4]
[2,2,1,1] => 110110 => [1,1,2,1,2] => [1,3,3]
[2,1,1,1,1] => 1011110 => [1,2,1,1,1,2] => [1,5,2]
[1,1,1,1,1,1] => 1111110 => [1,1,1,1,1,1,2] => [1,7]
[7] => 10000000 => [1,8] => [1,1,1,1,1,1,1,2]
[6,1] => 10000010 => [1,6,2] => [1,2,1,1,1,1,2]
[5,2] => 1000100 => [1,4,3] => [1,1,2,1,1,2]
[5,1,1] => 10000110 => [1,5,1,2] => [1,3,1,1,1,2]
[4,3] => 101000 => [1,2,4] => [1,1,1,2,2]
[4,2,1] => 1001010 => [1,3,2,2] => [1,2,2,1,2]
[4,1,1,1] => 10001110 => [1,4,1,1,2] => [1,4,1,1,2]
[3,3,1] => 110010 => [1,1,3,2] => [1,2,1,3]
[3,2,2] => 101100 => [1,2,1,3] => [1,1,3,2]
[3,2,1,1] => 1010110 => [1,2,2,1,2] => [1,3,2,2]
[3,1,1,1,1] => 10011110 => [1,3,1,1,1,2] => [1,5,1,2]
[2,2,2,1] => 111010 => [1,1,1,2,2] => [1,2,4]
[2,2,1,1,1] => 1101110 => [1,1,2,1,1,2] => [1,4,3]
[2,1,1,1,1,1] => 10111110 => [1,2,1,1,1,1,2] => [1,6,2]
[1,1,1,1,1,1,1] => 11111110 => [1,1,1,1,1,1,1,2] => [1,8]
[8] => 100000000 => [1,9] => [1,1,1,1,1,1,1,1,2]
[7,1] => 100000010 => [1,7,2] => [1,2,1,1,1,1,1,2]
[6,2] => 10000100 => [1,5,3] => [1,1,2,1,1,1,2]
[6,1,1] => 100000110 => [1,6,1,2] => [1,3,1,1,1,1,2]
[5,3] => 1001000 => [1,3,4] => [1,1,1,2,1,2]
[5,2,1] => 10001010 => [1,4,2,2] => [1,2,2,1,1,2]
[5,1,1,1] => 100001110 => [1,5,1,1,2] => [1,4,1,1,1,2]
[4,4] => 110000 => [1,1,5] => [1,1,1,1,3]
[4,3,1] => 1010010 => [1,2,3,2] => [1,2,1,2,2]
[4,2,2] => 1001100 => [1,3,1,3] => [1,1,3,1,2]
[4,2,1,1] => 10010110 => [1,3,2,1,2] => [1,3,2,1,2]
[4,1,1,1,1] => 100011110 => [1,4,1,1,1,2] => [1,5,1,1,2]
[3,3,2] => 110100 => [1,1,2,3] => [1,1,2,3]
[3,3,1,1] => 1100110 => [1,1,3,1,2] => [1,3,1,3]
[3,2,2,1] => 1011010 => [1,2,1,2,2] => [1,2,3,2]
[3,2,1,1,1] => 10101110 => [1,2,2,1,1,2] => [1,4,2,2]
[3,1,1,1,1,1] => 100111110 => [1,3,1,1,1,1,2] => [1,6,1,2]
[2,2,2,2] => 111100 => [1,1,1,1,3] => [1,1,5]
[2,2,2,1,1] => 1110110 => [1,1,1,2,1,2] => [1,3,4]
[2,2,1,1,1,1] => 11011110 => [1,1,2,1,1,1,2] => [1,5,3]
[2,1,1,1,1,1,1] => 101111110 => [1,2,1,1,1,1,1,2] => [1,7,2]
[1,1,1,1,1,1,1,1] => 111111110 => [1,1,1,1,1,1,1,1,2] => [1,9]
[9] => 1000000000 => [1,10] => [1,1,1,1,1,1,1,1,1,2]
[8,1] => 1000000010 => [1,8,2] => [1,2,1,1,1,1,1,1,2]
[7,2] => 100000100 => [1,6,3] => [1,1,2,1,1,1,1,2]
[7,1,1] => 1000000110 => [1,7,1,2] => [1,3,1,1,1,1,1,2]
[6,3] => 10001000 => [1,4,4] => [1,1,1,2,1,1,2]
[6,2,1] => 100001010 => [1,5,2,2] => [1,2,2,1,1,1,2]
[6,1,1,1] => 1000001110 => [1,6,1,1,2] => [1,4,1,1,1,1,2]
[5,4] => 1010000 => [1,2,5] => [1,1,1,1,2,2]
[5,3,1] => 10010010 => [1,3,3,2] => [1,2,1,2,1,2]
[5,2,2] => 10001100 => [1,4,1,3] => [1,1,3,1,1,2]
[5,2,1,1] => 100010110 => [1,4,2,1,2] => [1,3,2,1,1,2]
[5,1,1,1,1] => 1000011110 => [1,5,1,1,1,2] => [1,5,1,1,1,2]
[4,4,1] => 1100010 => [1,1,4,2] => [1,2,1,1,3]
[4,3,2] => 1010100 => [1,2,2,3] => [1,1,2,2,2]
[4,3,1,1] => 10100110 => [1,2,3,1,2] => [1,3,1,2,2]
[4,2,2,1] => 10011010 => [1,3,1,2,2] => [1,2,3,1,2]
[4,2,1,1,1] => 100101110 => [1,3,2,1,1,2] => [1,4,2,1,2]
[4,1,1,1,1,1] => 1000111110 => [1,4,1,1,1,1,2] => [1,6,1,1,2]
[3,3,3] => 111000 => [1,1,1,4] => [1,1,1,4]
[3,3,2,1] => 1101010 => [1,1,2,2,2] => [1,2,2,3]
[3,3,1,1,1] => 11001110 => [1,1,3,1,1,2] => [1,4,1,3]
[3,2,2,2] => 1011100 => [1,2,1,1,3] => [1,1,4,2]
[3,2,2,1,1] => 10110110 => [1,2,1,2,1,2] => [1,3,3,2]
[3,2,1,1,1,1] => 101011110 => [1,2,2,1,1,1,2] => [1,5,2,2]
[3,1,1,1,1,1,1] => 1001111110 => [1,3,1,1,1,1,1,2] => [1,7,1,2]
[2,2,2,2,1] => 1111010 => [1,1,1,1,2,2] => [1,2,5]
[2,2,2,1,1,1] => 11101110 => [1,1,1,2,1,1,2] => [1,4,4]
[2,2,1,1,1,1,1] => 110111110 => [1,1,2,1,1,1,1,2] => [1,6,3]
[2,1,1,1,1,1,1,1] => 1011111110 => [1,2,1,1,1,1,1,1,2] => [1,8,2]
[1,1,1,1,1,1,1,1,1] => 1111111110 => [1,1,1,1,1,1,1,1,1,2] => [1,10]
[10] => 10000000000 => [1,11] => [1,1,1,1,1,1,1,1,1,1,2]
[9,1] => 10000000010 => [1,9,2] => [1,2,1,1,1,1,1,1,1,2]
[8,2] => 1000000100 => [1,7,3] => [1,1,2,1,1,1,1,1,2]
[8,1,1] => 10000000110 => [1,8,1,2] => [1,3,1,1,1,1,1,1,2]
[7,3] => 100001000 => [1,5,4] => [1,1,1,2,1,1,1,2]
>>> Load all 404 entries. <<<Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending 1 to a binary word w, the i-th part of the composition equals 1 plus the number of zeros after the i-th 1 in w.
This map is not surjective, since the empty composition does not have a preimage.
Prepending 1 to a binary word w, the i-th part of the composition equals 1 plus the number of zeros after the i-th 1 in w.
This map is not surjective, since the empty composition does not have a preimage.
Map
conjugate
searching the database
Sorry, this map was not found in the database.