Processing math: 47%

Identifier
Values
[1,2,3] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[3,2,1] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[1,2,3,4] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[2,1,4,3] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[3,1,4,2] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[4,3,2,1] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[1,2,3,4,5] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[5,4,3,2,1] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[1,2,3,4,5,6] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[2,1,4,3,6,5] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[2,1,5,3,6,4] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[3,1,4,2,6,5] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[3,1,5,2,6,4] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[3,2,1,6,5,4] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[4,1,5,2,6,3] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[4,2,1,6,5,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[4,3,1,6,5,2] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[5,2,1,6,4,3] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[5,3,1,6,4,2] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[6,5,4,3,2,1] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[1,2,3,4,5,6,7] => [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) => 7
[7,6,5,4,3,2,1] => [7] => [[7],[]] => ([(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
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence u=(u1,u2,) is an index i such that ui<ui+1. Let asc(u) denote the number of ascents of u, and let
asc(u):={0if u is empty,1+asc(u)otherwise.
Given a permutation w in the symmetric group Sn, define
Ak:=max
where the maximum is taken over disjoint subsequences {u_i} of w.
Then A'_1, A'_2-A'_1, A'_3-A'_2,\dots is a partition of n. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
Map
to skew partition
Description
The partition regarded as a skew partition.
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.