Identifier
Values
00110 => [2,2,1] => [[3,3,2],[2,1]] => ([(0,2),(2,1)],3) => 3
01100 => [1,2,2] => [[3,2,1],[1]] => ([(0,2),(2,1)],3) => 3
10011 => [1,2,2] => [[3,2,1],[1]] => ([(0,2),(2,1)],3) => 3
11001 => [2,2,1] => [[3,3,2],[2,1]] => ([(0,2),(2,1)],3) => 3
000110 => [3,2,1] => [[4,4,3],[3,2]] => ([(0,2),(2,1)],3) => 3
000111 => [3,3] => [[5,3],[2]] => ([(0,2),(2,1)],3) => 3
001001 => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
001100 => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
001101 => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3) => 3
001110 => [2,3,1] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
010010 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => ([(0,2),(2,1)],3) => 3
010011 => [1,1,2,2] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => 3
011000 => [1,2,3] => [[4,2,1],[1]] => ([(0,2),(2,1)],3) => 3
011001 => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 4
011011 => [1,2,1,2] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
011100 => [1,3,2] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
100011 => [1,3,2] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
100100 => [1,2,1,2] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
100110 => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 4
100111 => [1,2,3] => [[4,2,1],[1]] => ([(0,2),(2,1)],3) => 3
101100 => [1,1,2,2] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => 3
101101 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => ([(0,2),(2,1)],3) => 3
110001 => [2,3,1] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
110010 => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3) => 3
110011 => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
110110 => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
111000 => [3,3] => [[5,3],[2]] => ([(0,2),(2,1)],3) => 3
111001 => [3,2,1] => [[4,4,3],[3,2]] => ([(0,2),(2,1)],3) => 3
0000110 => [4,2,1] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => 3
0000111 => [4,3] => [[6,4],[3]] => ([(0,2),(2,1)],3) => 3
0001000 => [3,1,3] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => 3
0001001 => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
0001100 => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
0001101 => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => 3
0001110 => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
0001111 => [3,4] => [[6,3],[2]] => ([(0,2),(2,1)],3) => 3
0010001 => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
0010010 => [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) => 4
0010011 => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 5
0010110 => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
0011000 => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
0011001 => [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) => 6
0011010 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => 3
0011011 => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 5
0011100 => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
0011101 => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
0011110 => [2,4,1] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
0100010 => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3) => 3
0100011 => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
0100100 => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 4
0100101 => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => 3
0100110 => [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) => 5
0100111 => [1,1,2,3] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 3
0101100 => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 3
0101101 => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 3
0110000 => [1,2,4] => [[5,2,1],[1]] => ([(0,2),(2,1)],3) => 3
0110001 => [1,2,3,1] => [[4,4,2,1],[3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5
0110010 => [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) => 5
0110011 => [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) => 6
0110100 => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
0110110 => [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) => 5
0110111 => [1,2,1,3] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
0111000 => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
0111001 => [1,3,2,1] => [[4,4,3,1],[3,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5
0111011 => [1,3,1,2] => [[4,3,3,1],[2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
0111100 => [1,4,2] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1000011 => [1,4,2] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1000100 => [1,3,1,2] => [[4,3,3,1],[2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
1000110 => [1,3,2,1] => [[4,4,3,1],[3,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5
1000111 => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
1001000 => [1,2,1,3] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1001001 => [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) => 5
1001011 => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1001100 => [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) => 6
1001101 => [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) => 5
1001110 => [1,2,3,1] => [[4,4,2,1],[3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5
1001111 => [1,2,4] => [[5,2,1],[1]] => ([(0,2),(2,1)],3) => 3
1010010 => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 3
1010011 => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 3
1011000 => [1,1,2,3] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 3
1011001 => [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) => 5
1011010 => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => 3
1011011 => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 4
1011100 => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1011101 => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3) => 3
1100001 => [2,4,1] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1100010 => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1100011 => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
1100100 => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 5
1100101 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => 3
1100110 => [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) => 6
1100111 => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
1101001 => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
1101100 => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 5
1101101 => [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) => 4
1101110 => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
1110000 => [3,4] => [[6,3],[2]] => ([(0,2),(2,1)],3) => 3
1110001 => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
1110010 => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => 3
1110011 => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
1110110 => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
>>> Load all 196 entries. <<<
1110111 => [3,1,3] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => 3
1111000 => [4,3] => [[6,4],[3]] => ([(0,2),(2,1)],3) => 3
1111001 => [4,2,1] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => 3
00001000 => [4,1,3] => [[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => 3
00001001 => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
00001100 => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
00001101 => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => 3
00001110 => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
00001111 => [4,4] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 4
00010001 => [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) => 5
00010010 => [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) => 4
00010110 => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
00010111 => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => 3
00011010 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => 3
00011011 => [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) => 6
00011101 => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
00011110 => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 4
00100010 => [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) => 5
00100101 => [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) => 4
00100111 => [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) => 6
00101001 => [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) => 3
00101100 => [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) => 5
00101101 => [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) => 4
00101110 => [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) => 4
00110100 => [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) => 5
00110101 => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => 3
00111010 => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
00111100 => [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) => 5
00111101 => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
01000100 => [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) => 5
01000111 => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
01001010 => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => 3
01001011 => [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) => 4
01001110 => [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) => 6
01010010 => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 3
01010011 => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 3
01011001 => [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) => 5
01011010 => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => 4
01011011 => [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) => 4
01011100 => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
01100101 => [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) => 5
01101001 => [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) => 5
01101011 => [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) => 3
01110010 => [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) => 6
01110100 => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
01110111 => [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) => 5
01111000 => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 4
01111001 => [1,4,2,1] => [[5,5,4,1],[4,3]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5
01111011 => [1,4,1,2] => [[5,4,4,1],[3,3]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
10000100 => [1,4,1,2] => [[5,4,4,1],[3,3]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
10000110 => [1,4,2,1] => [[5,5,4,1],[4,3]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 5
10000111 => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 4
10001000 => [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) => 5
10001011 => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 4
10001101 => [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) => 6
10010100 => [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) => 3
10010110 => [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) => 5
10011010 => [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) => 5
10100011 => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
10100100 => [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) => 4
10100101 => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => 4
10100110 => [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) => 5
10101100 => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 3
10101101 => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 3
10110001 => [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) => 6
10110100 => [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) => 4
10110101 => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => 3
10111000 => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
10111011 => [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) => 5
11000010 => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
11000011 => [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) => 5
11000101 => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
11001010 => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => 3
11001011 => [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) => 5
11010001 => [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) => 4
11010010 => [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) => 4
11010011 => [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) => 5
11010110 => [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) => 3
11011000 => [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) => 6
11011010 => [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) => 4
11011101 => [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) => 5
11100001 => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 4
11100010 => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
11100100 => [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) => 6
11100101 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => 3
11101000 => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => 3
11101001 => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
11101101 => [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) => 4
11101110 => [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) => 5
11110000 => [4,4] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 4
11110001 => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4
11110010 => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => 3
11110011 => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 5
11110110 => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
11110111 => [4,1,3] => [[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => 3
search for individual values
searching the database for the individual values of this statistic
Description
The number of simple modules with projective dimension at most 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
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.
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 $w$.