Loading [MathJax]/jax/output/HTML-CSS/jax.js

Identifier
Values
[[1]] => [1] => [[1],[]] => ([],1) => 1
[[1],[1]] => [1,1] => [[1,1],[]] => ([(0,1)],2) => 2
[[2]] => [2] => [[2],[]] => ([(0,1)],2) => 2
[[1,1]] => [2] => [[2],[]] => ([(0,1)],2) => 2
[[1],[1],[1]] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3
[[2],[1]] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 3
[[1,1],[1]] => [2,1] => [[2,1],[]] => ([(0,1),(0,2)],3) => 3
[[3]] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[[2,1]] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[[1,1,1]] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3
[[1],[1],[1],[1]] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[[2],[1],[1]] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 4
[[2],[2]] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[[1,1],[1],[1]] => [2,1,1] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => 4
[[1,1],[1,1]] => [2,2] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 4
[[3],[1]] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 4
[[2,1],[1]] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 4
[[1,1,1],[1]] => [3,1] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => 4
[[4]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[[3,1]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[[2,2]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[[2,1,1]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[[1,1,1,1]] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[2],[1],[1],[1]] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5
[[2],[2],[1]] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5
[[1,1],[1],[1],[1]] => [2,1,1,1] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5
[[1,1],[1,1],[1]] => [2,2,1] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5
[[3],[1],[1]] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 5
[[3],[2]] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5
[[2,1],[1],[1]] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 5
[[2,1],[2]] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5
[[2,1],[1,1]] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5
[[1,1,1],[1],[1]] => [3,1,1] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => 5
[[1,1,1],[1,1]] => [3,2] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 5
[[4],[1]] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5
[[3,1],[1]] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5
[[2,2],[1]] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5
[[2,1,1],[1]] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5
[[1,1,1,1],[1]] => [4,1] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => 5
[[5]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[4,1]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[3,2]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[3,1,1]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[2,2,1]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[2,1,1,1]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[1,1,1,1,1]] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[1],[1],[1],[1],[1],[1]] => [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],[1],[1],[1]] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[2],[2],[1],[1]] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[2],[2],[2]] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[1,1],[1,1],[1,1]] => [2,2,2] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[[3],[1],[1],[1]] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[3],[2],[1]] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 6
[[3],[3]] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[[2,1],[1],[1],[1]] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[2,1],[2],[1]] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 6
[[2,1],[1,1],[1]] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 6
[[2,1],[2,1]] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[1,1,1],[1,1],[1]] => [3,2,1] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 6
[[1,1,1],[1,1,1]] => [3,3] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 6
[[4],[1],[1]] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[4],[2]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[3,1],[1],[1]] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[3,1],[2]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[3,1],[1,1]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[2,2],[1],[1]] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[2,2],[2]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[2,2],[1,1]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[2,1,1],[1],[1]] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[2,1,1],[2]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[2,1,1],[1,1]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[1,1,1,1],[1],[1]] => [4,1,1] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 6
[[1,1,1,1],[1,1]] => [4,2] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 6
[[5],[1]] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[4,1],[1]] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[3,2],[1]] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[3,1,1],[1]] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[2,2,1],[1]] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[2,1,1,1],[1]] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[1,1,1,1,1],[1]] => [5,1] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 6
[[6]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[5,1]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[4,2]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[4,1,1]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[3,3]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[3,2,1]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[3,1,1,1]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[2,2,2]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[2,2,1,1]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[2,1,1,1,1]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[1,1,1,1,1,1]] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
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 elements in the poset.
Map
to partition
Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
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.