Identifier
Values
0 => [2] => [[2],[]] => ([],1) => 2
1 => [1,1] => [[1,1],[]] => ([],1) => 2
00 => [3] => [[3],[]] => ([],1) => 2
01 => [2,1] => [[2,2],[1]] => ([],1) => 2
10 => [1,2] => [[2,1],[]] => ([],1) => 2
11 => [1,1,1] => [[1,1,1],[]] => ([],1) => 2
000 => [4] => [[4],[]] => ([],1) => 2
001 => [3,1] => [[3,3],[2]] => ([],1) => 2
010 => [2,2] => [[3,2],[1]] => ([(0,1)],2) => 3
011 => [2,1,1] => [[2,2,2],[1,1]] => ([],1) => 2
100 => [1,3] => [[3,1],[]] => ([],1) => 2
101 => [1,2,1] => [[2,2,1],[1]] => ([(0,1)],2) => 3
110 => [1,1,2] => [[2,1,1],[]] => ([],1) => 2
111 => [1,1,1,1] => [[1,1,1,1],[]] => ([],1) => 2
0000 => [5] => [[5],[]] => ([],1) => 2
0001 => [4,1] => [[4,4],[3]] => ([],1) => 2
0010 => [3,2] => [[4,3],[2]] => ([(0,1)],2) => 3
0011 => [3,1,1] => [[3,3,3],[2,2]] => ([],1) => 2
0100 => [2,3] => [[4,2],[1]] => ([(0,1)],2) => 3
0101 => [2,2,1] => [[3,3,2],[2,1]] => ([(0,2),(2,1)],3) => 4
0110 => [2,1,2] => [[3,2,2],[1,1]] => ([(0,1)],2) => 3
0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => ([],1) => 2
1000 => [1,4] => [[4,1],[]] => ([],1) => 2
1001 => [1,3,1] => [[3,3,1],[2]] => ([(0,1)],2) => 3
1010 => [1,2,2] => [[3,2,1],[1]] => ([(0,2),(2,1)],3) => 4
1011 => [1,2,1,1] => [[2,2,2,1],[1,1]] => ([(0,1)],2) => 3
1100 => [1,1,3] => [[3,1,1],[]] => ([],1) => 2
1101 => [1,1,2,1] => [[2,2,1,1],[1]] => ([(0,1)],2) => 3
1110 => [1,1,1,2] => [[2,1,1,1],[]] => ([],1) => 2
1111 => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([],1) => 2
00000 => [6] => [[6],[]] => ([],1) => 2
00001 => [5,1] => [[5,5],[4]] => ([],1) => 2
00010 => [4,2] => [[5,4],[3]] => ([(0,1)],2) => 3
00011 => [4,1,1] => [[4,4,4],[3,3]] => ([],1) => 2
00100 => [3,3] => [[5,3],[2]] => ([(0,2),(2,1)],3) => 4
00101 => [3,2,1] => [[4,4,3],[3,2]] => ([(0,2),(2,1)],3) => 4
00110 => [3,1,2] => [[4,3,3],[2,2]] => ([(0,1)],2) => 3
00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => ([],1) => 2
01000 => [2,4] => [[5,2],[1]] => ([(0,1)],2) => 3
01001 => [2,3,1] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
01010 => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7
01011 => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3) => 4
01100 => [2,1,3] => [[4,2,2],[1,1]] => ([(0,1)],2) => 3
01101 => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
01110 => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => ([(0,1)],2) => 3
01111 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => ([],1) => 2
10000 => [1,5] => [[5,1],[]] => ([],1) => 2
10001 => [1,4,1] => [[4,4,1],[3]] => ([(0,1)],2) => 3
10010 => [1,3,2] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
10011 => [1,3,1,1] => [[3,3,3,1],[2,2]] => ([(0,1)],2) => 3
10100 => [1,2,3] => [[4,2,1],[1]] => ([(0,2),(2,1)],3) => 4
10101 => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7
10110 => [1,2,1,2] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
10111 => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => ([(0,1)],2) => 3
11000 => [1,1,4] => [[4,1,1],[]] => ([],1) => 2
11001 => [1,1,3,1] => [[3,3,1,1],[2]] => ([(0,1)],2) => 3
11010 => [1,1,2,2] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => 4
11011 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => ([(0,2),(2,1)],3) => 4
11100 => [1,1,1,3] => [[3,1,1,1],[]] => ([],1) => 2
11101 => [1,1,1,2,1] => [[2,2,1,1,1],[1]] => ([(0,1)],2) => 3
11110 => [1,1,1,1,2] => [[2,1,1,1,1],[]] => ([],1) => 2
11111 => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([],1) => 2
000000 => [7] => [[7],[]] => ([],1) => 2
000001 => [6,1] => [[6,6],[5]] => ([],1) => 2
000010 => [5,2] => [[6,5],[4]] => ([(0,1)],2) => 3
000011 => [5,1,1] => [[5,5,5],[4,4]] => ([],1) => 2
000100 => [4,3] => [[6,4],[3]] => ([(0,2),(2,1)],3) => 4
000101 => [4,2,1] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => 4
000110 => [4,1,2] => [[5,4,4],[3,3]] => ([(0,1)],2) => 3
000111 => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => ([],1) => 2
001000 => [3,4] => [[6,3],[2]] => ([(0,2),(2,1)],3) => 4
001001 => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7
001010 => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 9
001011 => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => 4
001100 => [3,1,3] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => 4
001101 => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
001110 => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => ([(0,1)],2) => 3
001111 => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => ([],1) => 2
010000 => [2,5] => [[6,2],[1]] => ([(0,1)],2) => 3
010001 => [2,4,1] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
010010 => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 9
010011 => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
010100 => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 9
010101 => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 15
010110 => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 10
010111 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => 4
011000 => [2,1,4] => [[5,2,2],[1,1]] => ([(0,1)],2) => 3
011001 => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 7
011010 => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 10
011011 => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7
011100 => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => ([(0,1)],2) => 3
011101 => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
011110 => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => ([(0,1)],2) => 3
011111 => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => ([],1) => 2
100000 => [1,6] => [[6,1],[]] => ([],1) => 2
100001 => [1,5,1] => [[5,5,1],[4]] => ([(0,1)],2) => 3
100010 => [1,4,2] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
100011 => [1,4,1,1] => [[4,4,4,1],[3,3]] => ([(0,1)],2) => 3
100100 => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7
100101 => [1,3,2,1] => [[4,4,3,1],[3,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 10
100110 => [1,3,1,2] => [[4,3,3,1],[2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 7
>>> Load all 226 entries. <<<
100111 => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => ([(0,1)],2) => 3
101000 => [1,2,4] => [[5,2,1],[1]] => ([(0,2),(2,1)],3) => 4
101001 => [1,2,3,1] => [[4,4,2,1],[3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 10
101010 => [1,2,2,2] => [[4,3,2,1],[2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 15
101011 => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 9
101100 => [1,2,1,3] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
101101 => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 9
101110 => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
101111 => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => ([(0,1)],2) => 3
110000 => [1,1,5] => [[5,1,1],[]] => ([],1) => 2
110001 => [1,1,4,1] => [[4,4,1,1],[3]] => ([(0,1)],2) => 3
110010 => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
110011 => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3) => 4
110100 => [1,1,2,3] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 4
110101 => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 9
110110 => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7
110111 => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => 4
111000 => [1,1,1,4] => [[4,1,1,1],[]] => ([],1) => 2
111001 => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => ([(0,1)],2) => 3
111010 => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 4
111011 => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 4
111100 => [1,1,1,1,3] => [[3,1,1,1,1],[]] => ([],1) => 2
111101 => [1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] => ([(0,1)],2) => 3
111110 => [1,1,1,1,1,2] => [[2,1,1,1,1,1],[]] => ([],1) => 2
111111 => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([],1) => 2
0000000 => [8] => [[8],[]] => ([],1) => 2
0001000 => [4,4] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 5
0001001 => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7
0001010 => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 9
0001011 => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => 4
0001100 => [4,1,3] => [[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => 4
0001101 => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
0001110 => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => ([(0,1)],2) => 3
0001111 => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => ([],1) => 2
0010001 => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
0010010 => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 20
0010011 => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7
0010100 => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 20
0010101 => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) => 36
0010110 => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 13
0010111 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => 4
0011001 => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 15
0011010 => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => 23
0011011 => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7
0011100 => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => 4
0011101 => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
0100010 => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 15
0100011 => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
0100100 => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 20
0100110 => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => 23
0100111 => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
0101011 => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) => 36
0101100 => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => 23
0101110 => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 10
0101111 => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => 4
0110010 => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => 23
0110011 => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 15
0110100 => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 13
0110110 => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) => 36
0110111 => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7
0111001 => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 7
0111010 => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 10
0111011 => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
0111101 => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
0111110 => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => ([(0,1)],2) => 3
1000000 => [1,7] => [[7,1],[]] => ([],1) => 2
1000100 => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
1000101 => [1,4,2,1] => [[5,5,4,1],[4,3]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 10
1000110 => [1,4,1,2] => [[5,4,4,1],[3,3]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 7
1000111 => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => ([(0,1)],2) => 3
1001001 => [1,3,3,1] => [[5,5,3,1],[4,2]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) => 36
1001011 => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 13
1001100 => [1,3,1,3] => [[5,3,3,1],[2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 15
1001101 => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => 23
1001110 => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 7
1010011 => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => 23
1010100 => [1,2,2,3] => [[5,3,2,1],[2,1]] => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) => 36
1010111 => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 9
1011001 => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => 23
1011011 => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 20
1011101 => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 15
1011110 => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
1011111 => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => ([(0,1)],2) => 3
1100000 => [1,1,6] => [[6,1,1],[]] => ([],1) => 2
1100100 => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 7
1100101 => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => 23
1100110 => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 15
1101001 => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 13
1101010 => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) => 36
1101011 => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 20
1101101 => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 20
1101110 => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 10
1101111 => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => 4
1110000 => [1,1,1,5] => [[5,1,1,1],[]] => ([],1) => 2
1110010 => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 5
1110101 => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 9
1110110 => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 7
1110111 => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => 5
1111000 => [1,1,1,1,4] => [[4,1,1,1,1],[]] => ([],1) => 2
1111010 => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 4
1111011 => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 4
1111100 => [1,1,1,1,1,3] => [[3,1,1,1,1,1],[]] => ([],1) => 2
1111101 => [1,1,1,1,1,2,1] => [[2,2,1,1,1,1,1],[1]] => ([(0,1)],2) => 3
1111110 => [1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1],[]] => ([],1) => 2
1111111 => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([],1) => 2
00000000 => [9] => [[9],[]] => ([],1) => 2
10000000 => [1,8] => [[8,1],[]] => ([],1) => 2
11000000 => [1,1,7] => [[7,1,1],[]] => ([],1) => 2
11100000 => [1,1,1,6] => [[6,1,1,1],[]] => ([],1) => 2
11110000 => [1,1,1,1,5] => [[5,1,1,1,1],[]] => ([],1) => 2
11111000 => [1,1,1,1,1,4] => [[4,1,1,1,1,1],[]] => ([],1) => 2
11111100 => [1,1,1,1,1,1,3] => [[3,1,1,1,1,1,1],[]] => ([],1) => 2
11111110 => [1,1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1,1],[]] => ([],1) => 2
11111111 => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([],1) => 2
000000000 => [10] => [[10],[]] => ([],1) => 2
100000000 => [1,9] => [[9,1],[]] => ([],1) => 2
110000000 => [1,1,8] => [[8,1,1],[]] => ([],1) => 2
111000000 => [1,1,1,7] => [[7,1,1,1],[]] => ([],1) => 2
111100000 => [1,1,1,1,6] => [[6,1,1,1,1],[]] => ([],1) => 2
111110000 => [1,1,1,1,1,5] => [[5,1,1,1,1,1],[]] => ([],1) => 2
111111000 => [1,1,1,1,1,1,4] => [[4,1,1,1,1,1,1],[]] => ([],1) => 2
111111100 => [1,1,1,1,1,1,1,3] => [[3,1,1,1,1,1,1,1],[]] => ([],1) => 2
111111110 => [1,1,1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1,1,1],[]] => ([],1) => 2
111111111 => [1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1],[]] => ([],1) => 2
=> [1] => [[1],[]] => ([],1) => 2
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Description
The number of non-isomorphic subposets of a lattice which are lattices.
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
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.
Map
dominating sublattice
Description
Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.