Identifier
Values
0 => 1 => ([(0,1)],2) => 1
1 => 0 => ([(0,1)],2) => 1
00 => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
01 => 00 => ([(0,2),(2,1)],3) => 1
10 => 11 => ([(0,2),(2,1)],3) => 1
11 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
001 => 000 => ([(0,3),(2,1),(3,2)],4) => 1
011 => 111 => ([(0,3),(2,1),(3,2)],4) => 1
0001 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
1011 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
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 number of connected components of the Hasse diagram for the poset.
Map
Gray next
Description
The next element in the Gray code for binary words.
Let $w$ be a binary word. If the number of ones in $w$ is even, return the binary word obtained by flipping the first bit of $w$. If the only one in $w$ is the final bit, return the zero word. Otherwise, return the word obtained by flipping the bit after the first one.
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 $v$.