Identifier
Values
0 => 0 => [1] => [[1],[]] => 1
1 => 1 => [1] => [[1],[]] => 1
00 => 00 => [2] => [[2],[]] => 2
01 => 01 => [1,1] => [[1,1],[]] => 2
10 => 01 => [1,1] => [[1,1],[]] => 2
11 => 11 => [2] => [[2],[]] => 2
000 => 000 => [3] => [[3],[]] => 2
001 => 001 => [2,1] => [[2,2],[1]] => 3
010 => 001 => [2,1] => [[2,2],[1]] => 3
011 => 011 => [1,2] => [[2,1],[]] => 3
100 => 001 => [2,1] => [[2,2],[1]] => 3
101 => 011 => [1,2] => [[2,1],[]] => 3
110 => 011 => [1,2] => [[2,1],[]] => 3
111 => 111 => [3] => [[3],[]] => 2
0000 => 0000 => [4] => [[4],[]] => 2
0001 => 0001 => [3,1] => [[3,3],[2]] => 3
0010 => 0001 => [3,1] => [[3,3],[2]] => 3
0011 => 0011 => [2,2] => [[3,2],[1]] => 4
0100 => 0001 => [3,1] => [[3,3],[2]] => 3
0101 => 0101 => [1,1,1,1] => [[1,1,1,1],[]] => 2
0110 => 0011 => [2,2] => [[3,2],[1]] => 4
0111 => 0111 => [1,3] => [[3,1],[]] => 3
1000 => 0001 => [3,1] => [[3,3],[2]] => 3
1001 => 0011 => [2,2] => [[3,2],[1]] => 4
1010 => 0011 => [2,2] => [[3,2],[1]] => 4
1011 => 0111 => [1,3] => [[3,1],[]] => 3
1100 => 0011 => [2,2] => [[3,2],[1]] => 4
1101 => 0111 => [1,3] => [[3,1],[]] => 3
1110 => 0111 => [1,3] => [[3,1],[]] => 3
1111 => 1111 => [4] => [[4],[]] => 2
00000 => 00000 => [5] => [[5],[]] => 2
00001 => 00001 => [4,1] => [[4,4],[3]] => 3
00010 => 00001 => [4,1] => [[4,4],[3]] => 3
00011 => 00011 => [3,2] => [[4,3],[2]] => 4
00100 => 00001 => [4,1] => [[4,4],[3]] => 3
00101 => 00101 => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 3
00110 => 00011 => [3,2] => [[4,3],[2]] => 4
00111 => 00111 => [2,3] => [[4,2],[1]] => 4
01000 => 00001 => [4,1] => [[4,4],[3]] => 3
01001 => 00101 => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 3
01010 => 00101 => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 3
01011 => 01011 => [1,1,1,2] => [[2,1,1,1],[]] => 3
01100 => 00011 => [3,2] => [[4,3],[2]] => 4
01101 => 01011 => [1,1,1,2] => [[2,1,1,1],[]] => 3
01110 => 00111 => [2,3] => [[4,2],[1]] => 4
01111 => 01111 => [1,4] => [[4,1],[]] => 3
10000 => 00001 => [4,1] => [[4,4],[3]] => 3
10001 => 00011 => [3,2] => [[4,3],[2]] => 4
10010 => 00011 => [3,2] => [[4,3],[2]] => 4
10011 => 00111 => [2,3] => [[4,2],[1]] => 4
10100 => 00011 => [3,2] => [[4,3],[2]] => 4
10101 => 01011 => [1,1,1,2] => [[2,1,1,1],[]] => 3
10110 => 00111 => [2,3] => [[4,2],[1]] => 4
10111 => 01111 => [1,4] => [[4,1],[]] => 3
11000 => 00011 => [3,2] => [[4,3],[2]] => 4
11001 => 00111 => [2,3] => [[4,2],[1]] => 4
11010 => 00111 => [2,3] => [[4,2],[1]] => 4
11011 => 01111 => [1,4] => [[4,1],[]] => 3
11100 => 00111 => [2,3] => [[4,2],[1]] => 4
11101 => 01111 => [1,4] => [[4,1],[]] => 3
11110 => 01111 => [1,4] => [[4,1],[]] => 3
11111 => 11111 => [5] => [[5],[]] => 2
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Description
The number of corners of a skew partition.
This is also known as the number of removable cells of the skew partition.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.