Identifier
Values
[1,2] => 0 => 0 => ([(0,1)],2) => 0
[2,1] => 1 => 1 => ([(0,1)],2) => 0
[1,2,3] => 00 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[1,3,2] => 01 => 00 => ([(0,2),(2,1)],3) => 0
[2,1,3] => 10 => 11 => ([(0,2),(2,1)],3) => 0
[2,3,1] => 01 => 00 => ([(0,2),(2,1)],3) => 0
[3,1,2] => 10 => 11 => ([(0,2),(2,1)],3) => 0
[3,2,1] => 11 => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[1,3,2,4] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 0
[1,4,2,3] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 0
[2,1,4,3] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 0
[2,3,1,4] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 0
[2,4,1,3] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 0
[3,1,4,2] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 0
[3,2,4,1] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 0
[3,4,1,2] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 0
[4,1,3,2] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 0
[4,2,3,1] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 0
[1,3,2,5,4] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,4,2,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,4,3,5,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,5,3,4,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,1,4,3,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,1,5,3,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,1,5,4] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,3,5,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,5,1,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,5,3,4,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,1,4,2,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,5,1,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,1,5,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,2,5,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,5,1,4,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,5,2,4,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,1,3,2,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,1,5,2,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,2,3,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,2,5,1,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,3,5,1,2] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,1,3,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[4,5,2,3,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,1,3,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,1,4,2,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,2,3,1,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,2,4,1,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[5,3,4,1,2] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,3,2,5,4,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,2,6,4,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,4,2,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,4,3,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,5,4,6,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,6,4,5,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,4,3,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,5,4,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,6,4,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,1,5,4,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,1,6,4,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,5,1,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,5,3,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,5,4,6,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,6,4,5,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,5,4,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,6,4,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,5,4,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,6,4,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
>>> Load all 172 entries. <<<
[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,5,4,6,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,6,1,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,6,2,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,6,4,5,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,1,3,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,3,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,5,3,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,5,2,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,6,1,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,3,6,2,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,1,3,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,1,6,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,2,3,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,2,6,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,5,3,6,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,1,3,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,1,5,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,2,3,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,2,5,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[4,6,3,5,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,1,3,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,1,4,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,1,4,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,1,6,2,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,1,6,3,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,3,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,4,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,4,3,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,6,1,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,2,6,3,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,4,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,4,2,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,6,1,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,3,6,2,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,4,6,1,3,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,4,6,2,3,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,6,1,3,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,6,1,4,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,6,2,3,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,6,2,4,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[5,6,3,4,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,1,3,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,1,4,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,1,4,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,1,5,2,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,1,5,3,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,2,3,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,2,4,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,2,4,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,2,5,1,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,2,5,3,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,3,4,1,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,3,4,2,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,3,5,1,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,3,5,2,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,4,5,1,3,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[6,4,5,2,3,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
Map
alternating inverse
Description
Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.