Identifier
Values
0 => ([(0,1)],2) => 1
1 => ([(0,1)],2) => 1
00 => ([(0,2),(2,1)],3) => 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
11 => ([(0,2),(2,1)],3) => 1
000 => ([(0,3),(2,1),(3,2)],4) => 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
111 => ([(0,3),(2,1),(3,2)],4) => 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1
00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1
000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1
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Description
The number of minimal elements in a poset.
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 $v$.