Identifier
Values
00 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
01 => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
10 => 11 => ([(0,2),(2,1)],3) => 3
11 => 00 => ([(0,2),(2,1)],3) => 3
000 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
011 => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
100 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
101 => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
110 => 111 => ([(0,3),(2,1),(3,2)],4) => 4
111 => 000 => ([(0,3),(2,1),(3,2)],4) => 4
1110 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
1111 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
11110 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
11111 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
111110 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
111111 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
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 $v$.
Map
path rowmotion
Description
Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.