Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000402
(load all 2 compositions to match this statistic)
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000402: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => [1,1,0,0]
 => [1,2] => 1
1 => [1,1] => [1,0,1,0]
 => [2,1] => 1
00 => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 1
01 => [2,1] => [1,1,0,0,1,0]
 => [3,1,2] => 2
10 => [1,2] => [1,0,1,1,0,0]
 => [2,3,1] => 2
11 => [1,1,1] => [1,0,1,0,1,0]
 => [3,2,1] => 1
000 => [4] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 1
001 => [3,1] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 2
010 => [2,2] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 1
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 2
100 => [1,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 1
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 2
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 1
0000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 1
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 2
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => 2
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => 2
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 2
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 2
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 1
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 2
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 2
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => 1
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => 2
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => 2
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => 2
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => 2
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => 1
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => 1
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [6,1,2,3,4,5] => 2
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [5,6,1,2,3,4] => 2
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [6,5,1,2,3,4] => 2
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [4,5,6,1,2,3] => 1
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [6,4,5,1,2,3] => 2
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [5,6,4,1,2,3] => 2
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [6,5,4,1,2,3] => 2
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [3,4,5,6,1,2] => 2
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [6,3,4,5,1,2] => 2
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [5,6,3,4,1,2] => 1
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [6,5,3,4,1,2] => 2
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [4,5,6,3,1,2] => 2
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [6,4,5,3,1,2] => 2
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [5,6,4,3,1,2] => 1
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,1,2] => 2
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => 2
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [6,2,3,4,5,1] => 1
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [5,6,2,3,4,1] => 2
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [6,5,2,3,4,1] => 2
Description
Half the size of the symmetry class of a permutation. The symmetry class of a permutation $\pi$ is the set of all permutations that can be obtained from $\pi$ by the three elementary operations '''inverse''' ([[Mp00066]]), '''reverse''' ([[Mp00064]]), and '''complement''' ([[Mp00069]]). This statistic is undefined for the unique permutation on one element, because its value would be $1/2$.
Matching statistic: St000260
Mapping
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 100%
Values
0 => 0 => [1] => ([],1)
 => 0 = 1 - 1
1 => 1 => [1] => ([],1)
 => 0 = 1 - 1
00 => 00 => [2] => ([],2)
 => ? = 1 - 1
01 => 10 => [1,1] => ([(0,1)],2)
 => 1 = 2 - 1
10 => 01 => [1,1] => ([(0,1)],2)
 => 1 = 2 - 1
11 => 11 => [2] => ([],2)
 => ? = 1 - 1
000 => 000 => [3] => ([],3)
 => ? = 1 - 1
001 => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
010 => 100 => [1,2] => ([(1,2)],3)
 => ? = 1 - 1
011 => 110 => [2,1] => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
100 => 001 => [2,1] => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
101 => 011 => [1,2] => ([(1,2)],3)
 => ? = 1 - 1
110 => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
111 => 111 => [3] => ([],3)
 => ? = 1 - 1
0000 => 0000 => [4] => ([],4)
 => ? = 1 - 1
0001 => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
0010 => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
0011 => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
0100 => 1000 => [1,3] => ([(2,3)],4)
 => ? = 2 - 1
0101 => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
0110 => 1100 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 - 1
0111 => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
1000 => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
1001 => 0011 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 - 1
1010 => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
1011 => 0111 => [1,3] => ([(2,3)],4)
 => ? = 2 - 1
1100 => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
1101 => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 - 1
1110 => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
1111 => 1111 => [4] => ([],4)
 => ? = 1 - 1
00000 => 00000 => [5] => ([],5)
 => ? = 1 - 1
00001 => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
00010 => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 - 1
00011 => 00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
00100 => 01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1 - 1
00101 => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
00110 => 01100 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 - 1
00111 => 01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
01000 => 10000 => [1,4] => ([(3,4)],5)
 => ? = 2 - 1
01001 => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
01010 => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 - 1
01011 => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
01100 => 11000 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2 - 1
01101 => 11010 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
01110 => 11100 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 - 1
01111 => 11110 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
10000 => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
10001 => 00011 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 - 1
10010 => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
10011 => 00111 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 2 - 1
10100 => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
10101 => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 - 1
10110 => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
10111 => 01111 => [1,4] => ([(3,4)],5)
 => ? = 2 - 1
11000 => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
11001 => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 - 1
11010 => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
11011 => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1 - 1
11100 => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
11101 => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 - 1
11110 => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
11111 => 11111 => [5] => ([],5)
 => ? = 1 - 1
000000 => 000000 => [6] => ([],6)
 => ? = 1 - 1
000001 => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
000010 => 000100 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 - 1
000011 => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
000100 => 001000 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 - 1
000101 => 001010 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
000111 => 001110 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
001001 => 010010 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
001010 => 010100 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 - 1
001011 => 010110 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
001111 => 011110 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
010000 => 100000 => [1,5] => ([(4,5)],6)
 => ? = 2 - 1
010101 => 101010 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
010111 => 101110 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
011111 => 111110 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 2 - 1
100000 => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 2 - 1
111111 => 111111 => [6] => ([],6)
 => ? = 1 - 1
0000000 => 0000000 => [7] => ([],7)
 => ? = 1 - 1
0000001 => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
0000010 => 0000100 => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
0000011 => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
0000100 => 0001000 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
0000101 => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
0000111 => 0001110 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
0001000 => 0010000 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 - 1
0001001 => 0010010 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
0001010 => 0010100 => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
0001011 => 0010110 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
0001111 => 0011110 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 2 - 1
0010010 => 0100100 => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
0011100 => 0111000 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 - 1
0100000 => 1000000 => [1,6] => ([(5,6)],7)
 => ? = 2 - 1
0100010 => 1000100 => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 - 1
0101000 => 1010000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
0101010 => 1010100 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 - 1
0111110 => 1111100 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 1 - 1
1001001 => 0010011 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 - 1
1010111 => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 - 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000526
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000526: Posets ⟶ ℤResult quality: 34% ●values known / values provided: 34%●distinct values known / distinct values provided: 100%
Values
0 => [2] => [[2],[]]
 => ([(0,1)],2)
 => 1
1 => [1,1] => [[1,1],[]]
 => ([(0,1)],2)
 => 1
00 => [3] => [[3],[]]
 => ([(0,2),(2,1)],3)
 => 1
01 => [2,1] => [[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => 2
10 => [1,2] => [[2,1],[]]
 => ([(0,1),(0,2)],3)
 => 2
11 => [1,1,1] => [[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => 1
000 => [4] => [[4],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
001 => [3,1] => [[3,3],[2]]
 => ([(0,3),(1,2),(2,3)],4)
 => 2
010 => [2,2] => [[3,2],[1]]
 => ([(0,3),(1,2),(1,3)],4)
 => 1
011 => [2,1,1] => [[2,2,2],[1,1]]
 => ([(0,3),(1,2),(2,3)],4)
 => 2
100 => [1,3] => [[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 2
101 => [1,2,1] => [[2,2,1],[1]]
 => ([(0,3),(1,2),(1,3)],4)
 => 1
110 => [1,1,2] => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 2
111 => [1,1,1,1] => [[1,1,1,1],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
0000 => [5] => [[5],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
0001 => [4,1] => [[4,4],[3]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 2
0010 => [3,2] => [[4,3],[2]]
 => ([(0,3),(1,2),(1,4),(3,4)],5)
 => 2
0011 => [3,1,1] => [[3,3,3],[2,2]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => 2
0100 => [2,3] => [[4,2],[1]]
 => ([(0,4),(1,2),(1,4),(2,3)],5)
 => 2
0101 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
0110 => [2,1,2] => [[3,2,2],[1,1]]
 => ([(0,4),(1,2),(1,3),(3,4)],5)
 => 1
0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 2
1000 => [1,4] => [[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 2
1001 => [1,3,1] => [[3,3,1],[2]]
 => ([(0,4),(1,2),(1,3),(3,4)],5)
 => 1
1010 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => 2
1011 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => ([(0,3),(1,2),(1,4),(3,4)],5)
 => 2
1100 => [1,1,3] => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 2
1101 => [1,1,2,1] => [[2,2,1,1],[1]]
 => ([(0,4),(1,2),(1,4),(2,3)],5)
 => 2
1110 => [1,1,1,2] => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 2
1111 => [1,1,1,1,1] => [[1,1,1,1,1],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
00000 => [6] => [[6],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
00001 => [5,1] => [[5,5],[4]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => 2
00010 => [4,2] => [[5,4],[3]]
 => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
 => 2
00011 => [4,1,1] => [[4,4,4],[3,3]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => 2
00100 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => 1
00101 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 2
00110 => [3,1,2] => [[4,3,3],[2,2]]
 => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
 => 2
00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => 2
01000 => [2,4] => [[5,2],[1]]
 => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => 2
01001 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 2
01010 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => 1
01011 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 2
01100 => [2,1,3] => [[4,2,2],[1,1]]
 => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6)
 => 2
01101 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 2
01110 => [2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => 1
01111 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => 2
10000 => [1,5] => [[5,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 2
10001 => [1,4,1] => [[4,4,1],[3]]
 => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
 => 1
10010 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
 => 2
10011 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
 => 2
000000 => [7] => [[7],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ? = 1
000001 => [6,1] => [[6,6],[5]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 2
000010 => [5,2] => [[6,5],[4]]
 => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
 => ? = 2
000011 => [5,1,1] => [[5,5,5],[4,4]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ? = 2
000100 => [4,3] => [[6,4],[3]]
 => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
 => ? = 2
000101 => [4,2,1] => [[5,5,4],[4,3]]
 => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
 => ? = 2
000111 => [4,1,1,1] => [[4,4,4,4],[3,3,3]]
 => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
 => ? = 2
001001 => [3,3,1] => [[5,5,3],[4,2]]
 => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7)
 => ? = 2
001010 => [3,2,2] => [[5,4,3],[3,2]]
 => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7)
 => ? = 2
001011 => [3,2,1,1] => [[4,4,4,3],[3,3,2]]
 => ([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7)
 => ? = 2
001111 => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ? = 2
010000 => [2,5] => [[6,2],[1]]
 => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
 => ? = 2
010111 => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]]
 => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
 => ? = 2
011111 => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 2
100000 => [1,6] => [[6,1],[]]
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ? = 2
111111 => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ? = 1
0000000 => [8] => [[8],[]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 1
0000001 => [7,1] => [[7,7],[6]]
 => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
 => ? = 2
0000010 => [6,2] => [[7,6],[5]]
 => ?
 => ? = 2
0000011 => [6,1,1] => [[6,6,6],[5,5]]
 => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
 => ? = 2
0000100 => [5,3] => [[7,5],[4]]
 => ?
 => ? = 2
0000101 => [5,2,1] => [[6,6,5],[5,4]]
 => ?
 => ? = 2
0000111 => [5,1,1,1] => [[5,5,5,5],[4,4,4]]
 => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
 => ? = 2
0001000 => [4,4] => [[7,4],[3]]
 => ([(0,5),(1,6),(1,7),(3,7),(4,2),(5,3),(6,4)],8)
 => ? = 1
0001001 => [4,3,1] => [[6,6,4],[5,3]]
 => ([(0,7),(1,4),(2,3),(2,6),(3,7),(4,5),(5,6)],8)
 => ? = 2
0001010 => [4,2,2] => [[6,5,4],[4,3]]
 => ([(0,6),(0,7),(1,4),(2,3),(2,6),(4,5),(5,7)],8)
 => ? = 2
0001011 => [4,2,1,1] => [[5,5,5,4],[4,4,3]]
 => ([(0,6),(0,7),(1,3),(2,4),(3,7),(4,5),(5,6)],8)
 => ? = 2
0001111 => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]]
 => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
 => ? = 2
0010010 => [3,3,2] => [[6,5,3],[4,2]]
 => ([(0,5),(1,4),(1,7),(2,3),(2,6),(4,6),(5,7)],8)
 => ? = 2
0010011 => [3,3,1,1] => [[5,5,5,3],[4,4,2]]
 => ([(0,3),(1,5),(2,4),(2,6),(3,7),(4,7),(5,6)],8)
 => ? = 2
0010101 => [3,2,2,1] => [[5,5,4,3],[4,3,2]]
 => ([(0,5),(1,6),(1,7),(2,5),(2,6),(3,4),(4,7)],8)
 => ? = 2
0010111 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]]
 => ([(0,6),(0,7),(1,3),(2,4),(3,7),(4,5),(5,6)],8)
 => ? = 2
0011001 => [3,1,3,1] => [[5,5,3,3],[4,2,2]]
 => ([(0,6),(1,4),(2,3),(2,5),(3,7),(4,7),(5,6)],8)
 => ? = 2
0011100 => [3,1,1,3] => [[5,3,3,3],[2,2,2]]
 => ([(0,4),(1,5),(1,6),(3,7),(4,7),(5,2),(6,3)],8)
 => ? = 1
0011111 => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]]
 => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
 => ? = 2
0100000 => [2,6] => [[7,2],[1]]
 => ?
 => ? = 2
0100010 => [2,4,2] => [[6,5,2],[4,1]]
 => ([(0,6),(1,4),(1,6),(2,3),(2,7),(4,5),(5,7)],8)
 => ? = 1
0101000 => [2,2,4] => [[6,3,2],[2,1]]
 => ?
 => ? = 2
0101010 => [2,2,2,2] => [[5,4,3,2],[3,2,1]]
 => ([(0,6),(1,5),(1,6),(2,5),(2,7),(3,4),(3,7)],8)
 => ? = 1
0101011 => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]]
 => ([(0,5),(1,6),(1,7),(2,5),(2,6),(3,4),(4,7)],8)
 => ? = 2
0101111 => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]]
 => ([(0,3),(1,6),(2,6),(2,7),(3,5),(4,7),(5,4)],8)
 => ? = 2
0110111 => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]]
 => ([(0,7),(1,4),(2,3),(2,6),(3,7),(4,5),(5,6)],8)
 => ? = 2
0111011 => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]]
 => ([(0,6),(1,3),(2,4),(2,7),(3,7),(4,5),(5,6)],8)
 => ? = 2
0111101 => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]]
 => ([(0,7),(1,6),(2,3),(2,6),(3,5),(4,7),(5,4)],8)
 => ? = 2
0111110 => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]]
 => ([(0,7),(1,2),(1,6),(3,7),(4,5),(5,3),(6,4)],8)
 => ? = 1
0111111 => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]]
 => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
 => ? = 2
1000000 => [1,7] => [[7,1],[]]
 => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 2
1001001 => [1,3,3,1] => [[5,5,3,1],[4,2]]
 => ([(0,6),(1,5),(1,7),(2,3),(2,4),(4,7),(5,6)],8)
 => ? = 1
1001100 => [1,3,1,3] => [[5,3,3,1],[2,2]]
 => ([(0,3),(0,4),(1,5),(1,6),(4,7),(5,7),(6,2)],8)
 => ? = 2
1010111 => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]]
 => ([(0,6),(0,7),(1,4),(2,3),(2,6),(4,5),(5,7)],8)
 => ? = 2
Description
The number of posets with combinatorially isomorphic order polytopes.