Identifier
Values
000 => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 2
010 => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 2
101 => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 2
111 => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 2
0000 => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 3
0101 => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 3
1010 => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 3
1111 => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 3
00000 => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
01010 => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
10101 => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
11111 => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
000000 => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
010101 => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
101010 => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
111111 => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
0000000 => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
0101010 => [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) => 6
1010101 => [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) => 6
1111111 => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.