Identifier
Values
001 => [2,1] => [[2,2],[1]] => [1] => 0
110 => [2,1] => [[2,2],[1]] => [1] => 0
0001 => [3,1] => [[3,3],[2]] => [2] => 1
0010 => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0
0011 => [2,2] => [[3,2],[1]] => [1] => 0
0110 => [1,2,1] => [[2,2,1],[1]] => [1] => 0
1001 => [1,2,1] => [[2,2,1],[1]] => [1] => 0
1100 => [2,2] => [[3,2],[1]] => [1] => 0
1101 => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0
1110 => [3,1] => [[3,3],[2]] => [2] => 1
00001 => [4,1] => [[4,4],[3]] => [3] => 0
00010 => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 2
00011 => [3,2] => [[4,3],[2]] => [2] => 1
00100 => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 0
00101 => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 0
00110 => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
00111 => [2,3] => [[4,2],[1]] => [1] => 0
01001 => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0
01100 => [1,2,2] => [[3,2,1],[1]] => [1] => 0
01101 => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0
01110 => [1,3,1] => [[3,3,1],[2]] => [2] => 1
10001 => [1,3,1] => [[3,3,1],[2]] => [2] => 1
10010 => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0
10011 => [1,2,2] => [[3,2,1],[1]] => [1] => 0
10110 => [1,1,2,1] => [[2,2,1,1],[1]] => [1] => 0
11000 => [2,3] => [[4,2],[1]] => [1] => 0
11001 => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
11010 => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 0
11011 => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 0
11100 => [3,2] => [[4,3],[2]] => [2] => 1
11101 => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 2
11110 => [4,1] => [[4,4],[3]] => [3] => 0
000001 => [5,1] => [[5,5],[4]] => [4] => 0
000010 => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 0
000011 => [4,2] => [[5,4],[3]] => [3] => 0
000100 => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
000101 => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 3
000110 => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
000111 => [3,3] => [[5,3],[2]] => [2] => 1
001000 => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 0
001001 => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
001010 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
001011 => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 0
001100 => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
001101 => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
001110 => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 0
001111 => [2,4] => [[5,2],[1]] => [1] => 0
010001 => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
010010 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 0
010011 => [1,1,2,2] => [[3,2,1,1],[1]] => [1] => 0
010110 => [1,1,1,2,1] => [[2,2,1,1,1],[1]] => [1] => 0
011000 => [1,2,3] => [[4,2,1],[1]] => [1] => 0
011001 => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
011010 => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 0
011011 => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 0
011100 => [1,3,2] => [[4,3,1],[2]] => [2] => 1
011101 => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 2
011110 => [1,4,1] => [[4,4,1],[3]] => [3] => 0
100001 => [1,4,1] => [[4,4,1],[3]] => [3] => 0
100010 => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 2
100011 => [1,3,2] => [[4,3,1],[2]] => [2] => 1
100100 => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 0
100101 => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 0
100110 => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
100111 => [1,2,3] => [[4,2,1],[1]] => [1] => 0
101001 => [1,1,1,2,1] => [[2,2,1,1,1],[1]] => [1] => 0
101100 => [1,1,2,2] => [[3,2,1,1],[1]] => [1] => 0
101101 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 0
101110 => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
110000 => [2,4] => [[5,2],[1]] => [1] => 0
110001 => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 0
110010 => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
110011 => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
110100 => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 0
110101 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
110110 => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
110111 => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 0
111000 => [3,3] => [[5,3],[2]] => [2] => 1
111001 => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
111010 => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 3
111011 => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
111100 => [4,2] => [[5,4],[3]] => [3] => 0
111101 => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 0
111110 => [5,1] => [[5,5],[4]] => [4] => 0
0000001 => [6,1] => [[6,6],[5]] => [5] => 0
0000010 => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 0
0000011 => [5,2] => [[6,5],[4]] => [4] => 0
0000100 => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 0
0000101 => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 0
0000110 => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 0
0000111 => [4,3] => [[6,4],[3]] => [3] => 0
0001000 => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
0001001 => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 2
0001010 => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 4
0001011 => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 3
0001100 => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
0001101 => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 1
0001110 => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 1
0001111 => [3,4] => [[6,3],[2]] => [2] => 1
0010000 => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 0
0010001 => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 0
>>> Load all 394 entries. <<<
0010010 => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 2
0010011 => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
0010100 => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
0010101 => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
0010110 => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
0010111 => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 0
0011000 => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
0011001 => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 1
0011010 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 3
0011011 => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
0011100 => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
0011101 => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 0
0011110 => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
0011111 => [2,5] => [[6,2],[1]] => [1] => 0
0100001 => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 0
0100010 => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 2
0100011 => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
0100100 => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 0
0100101 => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
0100110 => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
0100111 => [1,1,2,3] => [[4,2,1,1],[1]] => [1] => 0
0101001 => [1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] => [1] => 0
0101100 => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => [1] => 0
0101101 => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 0
0101110 => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
0110000 => [1,2,4] => [[5,2,1],[1]] => [1] => 0
0110001 => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 0
0110010 => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
0110011 => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
0110100 => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 0
0110101 => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
0110110 => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
0110111 => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 0
0111000 => [1,3,3] => [[5,3,1],[2]] => [2] => 1
0111001 => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 1
0111010 => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 3
0111011 => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 2
0111100 => [1,4,2] => [[5,4,1],[3]] => [3] => 0
0111101 => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 0
0111110 => [1,5,1] => [[5,5,1],[4]] => [4] => 0
1000001 => [1,5,1] => [[5,5,1],[4]] => [4] => 0
1000010 => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 0
1000011 => [1,4,2] => [[5,4,1],[3]] => [3] => 0
1000100 => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 2
1000101 => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 3
1000110 => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 1
1000111 => [1,3,3] => [[5,3,1],[2]] => [2] => 1
1001000 => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 0
1001001 => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
1001010 => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
1001011 => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 0
1001100 => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
1001101 => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
1001110 => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 0
1001111 => [1,2,4] => [[5,2,1],[1]] => [1] => 0
1010001 => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
1010010 => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 0
1010011 => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => [1] => 0
1010110 => [1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] => [1] => 0
1011000 => [1,1,2,3] => [[4,2,1,1],[1]] => [1] => 0
1011001 => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
1011010 => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
1011011 => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 0
1011100 => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
1011101 => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 2
1011110 => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 0
1100000 => [2,5] => [[6,2],[1]] => [1] => 0
1100001 => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
1100010 => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 0
1100011 => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
1100100 => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
1100101 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 3
1100110 => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 1
1100111 => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
1101000 => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 0
1101001 => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
1101010 => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
1101011 => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
1101100 => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
1101101 => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 2
1101110 => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 0
1101111 => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 0
1110000 => [3,4] => [[6,3],[2]] => [2] => 1
1110001 => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 1
1110010 => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 1
1110011 => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
1110100 => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 3
1110101 => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 4
1110110 => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 2
1110111 => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
1111000 => [4,3] => [[6,4],[3]] => [3] => 0
1111001 => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 0
1111010 => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 0
1111011 => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 0
1111100 => [5,2] => [[6,5],[4]] => [4] => 0
1111101 => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 0
1111110 => [6,1] => [[6,6],[5]] => [5] => 0
00000001 => [7,1] => [[7,7],[6]] => [6] => 0
00000010 => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 0
00000101 => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 0
00001000 => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 0
00001001 => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 0
00001010 => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 0
00001011 => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 0
00001100 => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 0
00001101 => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 0
00001110 => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 0
00001111 => [4,4] => [[7,4],[3]] => [3] => 0
00010001 => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 2
00010010 => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 2
00010011 => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 2
00010101 => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 5
00010110 => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 3
00010111 => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 3
00011000 => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 1
00011001 => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 1
00011010 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 1
00011011 => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 1
00011100 => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 1
00011101 => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 1
00011110 => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 1
00100010 => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 0
00100011 => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 0
00100100 => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 2
00100101 => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 3
00100110 => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 1
00100111 => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
00101001 => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
00101010 => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
00101011 => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
00101100 => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
00101101 => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 2
00101110 => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 0
00110001 => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 1
00110010 => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 1
00110011 => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 1
00110100 => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 3
00110101 => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 4
00110110 => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 2
00110111 => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
00111000 => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 0
00111001 => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 0
00111010 => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 0
00111011 => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 0
00111100 => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 0
00111101 => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 0
01000100 => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 2
01000110 => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 1
01000111 => [1,1,3,3] => [[5,3,1,1],[2]] => [2] => 1
01001001 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
01001010 => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
01001011 => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
01001100 => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [2,1] => 1
01001101 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
01001110 => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 0
01010010 => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 0
01010011 => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => [1] => 0
01010110 => [1,1,1,1,1,2,1] => [[2,2,1,1,1,1,1],[1]] => [1] => 0
01011001 => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
01011010 => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 0
01011011 => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => [1,1] => 0
01011100 => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [2] => 1
01100010 => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 0
01100011 => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 0
01100100 => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
01100101 => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 3
01100110 => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 1
01100111 => [1,2,2,3] => [[5,3,2,1],[2,1]] => [2,1] => 1
01101001 => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
01101010 => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
01101011 => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
01101100 => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
01101101 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 2
01101110 => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 0
01110001 => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 1
01110010 => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 1
01110011 => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 1
01110100 => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 3
01110110 => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 2
01110111 => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 2
01111000 => [1,4,3] => [[6,4,1],[3]] => [3] => 0
01111001 => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 0
01111010 => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 0
01111011 => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 0
10000100 => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 0
10000101 => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 0
10000110 => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 0
10000111 => [1,4,3] => [[6,4,1],[3]] => [3] => 0
10001000 => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 2
10001001 => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 2
10001011 => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 3
10001100 => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 1
10001101 => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 1
10001110 => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 1
10010001 => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 0
10010010 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 2
10010011 => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
10010100 => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
10010101 => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
10010110 => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
10011000 => [1,2,2,3] => [[5,3,2,1],[2,1]] => [2,1] => 1
10011001 => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 1
10011010 => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 3
10011011 => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
10011100 => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 0
10011101 => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 0
10100011 => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [2] => 1
10100100 => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => [1,1] => 0
10100101 => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 0
10100110 => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
10101001 => [1,1,1,1,1,2,1] => [[2,2,1,1,1,1,1],[1]] => [1] => 0
10101100 => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => [1] => 0
10101101 => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 0
10110001 => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 0
10110010 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
10110011 => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [2,1] => 1
10110100 => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
10110101 => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
10110110 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
10111000 => [1,1,3,3] => [[5,3,1,1],[2]] => [2] => 1
10111001 => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 1
10111011 => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 2
11000010 => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 0
11000011 => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 0
11000100 => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 0
11000101 => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 0
11000110 => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 0
11000111 => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 0
11001000 => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
11001001 => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 2
11001010 => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 4
11001011 => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 3
11001100 => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 1
11001101 => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 1
11001110 => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 1
11010001 => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 0
11010010 => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 2
11010011 => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
11010100 => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
11010101 => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
11010110 => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
11011000 => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
11011001 => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 1
11011010 => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 3
11011011 => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 2
11011100 => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 0
11011101 => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 0
11100001 => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 1
11100010 => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 1
11100011 => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 1
11100100 => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 1
11100101 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 1
11100110 => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 1
11100111 => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 1
11101000 => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 3
11101001 => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 3
11101010 => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 5
11101100 => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 2
11101101 => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 2
11101110 => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 2
11110000 => [4,4] => [[7,4],[3]] => [3] => 0
11110001 => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 0
11110010 => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 0
11110011 => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 0
11110100 => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 0
11110101 => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 0
11110110 => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 0
11110111 => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 0
11111010 => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 0
11111101 => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 0
11111110 => [7,1] => [[7,7],[6]] => [6] => 0
000000001 => [8,1] => [[8,8],[7]] => [7] => 0
000000010 => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 0
000000101 => [6,1,1,1] => [[6,6,6,6],[5,5,5]] => [5,5,5] => 0
000001010 => [5,1,1,1,1] => [[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4] => 0
000010101 => [4,1,1,1,1,1] => [[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3] => 0
000101010 => [3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 6
001010101 => [2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
110101010 => [2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
111010101 => [3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 6
111101010 => [4,1,1,1,1,1] => [[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3] => 0
111110101 => [5,1,1,1,1] => [[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4] => 0
111111010 => [6,1,1,1] => [[6,6,6,6],[5,5,5]] => [5,5,5] => 0
111111101 => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 0
111111110 => [8,1] => [[8,8],[7]] => [7] => 0
1111111110 => [9,1] => [[9,9],[8]] => [8] => 0
1111111101 => [8,1,1] => [[8,8,8],[7,7]] => [7,7] => 0
1110101010 => [3,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [2,2,2,2,2,2,2] => 7
1101010101 => [2,1,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
0000000001 => [9,1] => [[9,9],[8]] => [8] => 0
0010101010 => [2,1,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
0000000010 => [8,1,1] => [[8,8,8],[7,7]] => [7,7] => 0
0001010101 => [3,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [2,2,2,2,2,2,2] => 7
search for individual values
searching the database for the individual values of this statistic
Description
The number of twos in an integer partition.
The total number of twos in all partitions of $n$ is equal to the total number of singletons St001484The number of singletons of an integer partition. in all partitions of $n-1$, see [1].
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
inner shape
Description
The inner shape of a skew partition.
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 $w$.