Identifier
Values
([2],3) => [2] => [1,0,1,0] => 2
([1,1],3) => [1,1] => [1,1,0,0] => 2
([3,1],3) => [2,1] => [1,0,1,1,0,0] => 3
([2,1,1],3) => [1,1,1] => [1,1,0,1,0,0] => 3
([4,2],3) => [2,2] => [1,1,1,0,0,0] => 4
([3,1,1],3) => [2,1,1] => [1,0,1,1,0,1,0,0] => 4
([2,2,1,1],3) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 4
([5,3,1],3) => [2,2,1] => [1,1,1,0,0,1,0,0] => 5
([4,2,1,1],3) => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 5
([3,2,2,1,1],3) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 5
([6,4,2],3) => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
([5,3,1,1],3) => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 6
([4,2,2,1,1],3) => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 6
([3,3,2,2,1,1],3) => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 6
([2],4) => [2] => [1,0,1,0] => 2
([1,1],4) => [1,1] => [1,1,0,0] => 2
([3],4) => [3] => [1,0,1,0,1,0] => 3
([2,1],4) => [2,1] => [1,0,1,1,0,0] => 3
([1,1,1],4) => [1,1,1] => [1,1,0,1,0,0] => 3
([4,1],4) => [3,1] => [1,0,1,0,1,1,0,0] => 4
([2,2],4) => [2,2] => [1,1,1,0,0,0] => 4
([3,1,1],4) => [2,1,1] => [1,0,1,1,0,1,0,0] => 4
([2,1,1,1],4) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 4
([5,2],4) => [3,2] => [1,0,1,1,1,0,0,0] => 5
([4,1,1],4) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 5
([3,2,1],4) => [2,2,1] => [1,1,1,0,0,1,0,0] => 5
([3,1,1,1],4) => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 5
([2,2,1,1,1],4) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 5
([6,3],4) => [3,3] => [1,1,1,0,1,0,0,0] => 6
([5,2,1],4) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 6
([4,1,1,1],4) => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 6
([4,2,2],4) => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
([3,3,1,1],4) => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 6
([3,2,1,1,1],4) => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 6
([2,2,2,1,1,1],4) => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 6
([2],5) => [2] => [1,0,1,0] => 2
([1,1],5) => [1,1] => [1,1,0,0] => 2
([3],5) => [3] => [1,0,1,0,1,0] => 3
([2,1],5) => [2,1] => [1,0,1,1,0,0] => 3
([1,1,1],5) => [1,1,1] => [1,1,0,1,0,0] => 3
([4],5) => [4] => [1,0,1,0,1,0,1,0] => 4
([3,1],5) => [3,1] => [1,0,1,0,1,1,0,0] => 4
([2,2],5) => [2,2] => [1,1,1,0,0,0] => 4
([2,1,1],5) => [2,1,1] => [1,0,1,1,0,1,0,0] => 4
([1,1,1,1],5) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 4
([5,1],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 5
([3,2],5) => [3,2] => [1,0,1,1,1,0,0,0] => 5
([4,1,1],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 5
([2,2,1],5) => [2,2,1] => [1,1,1,0,0,1,0,0] => 5
([3,1,1,1],5) => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 5
([2,1,1,1,1],5) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 5
([6,2],5) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 6
([5,1,1],5) => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 6
([3,3],5) => [3,3] => [1,1,1,0,1,0,0,0] => 6
([4,2,1],5) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 6
([4,1,1,1],5) => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 6
([2,2,2],5) => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
([3,2,1,1],5) => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 6
([3,1,1,1,1],5) => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 6
([2,2,1,1,1,1],5) => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 6
([2],6) => [2] => [1,0,1,0] => 2
([1,1],6) => [1,1] => [1,1,0,0] => 2
([3],6) => [3] => [1,0,1,0,1,0] => 3
([2,1],6) => [2,1] => [1,0,1,1,0,0] => 3
([1,1,1],6) => [1,1,1] => [1,1,0,1,0,0] => 3
([4],6) => [4] => [1,0,1,0,1,0,1,0] => 4
([3,1],6) => [3,1] => [1,0,1,0,1,1,0,0] => 4
([2,2],6) => [2,2] => [1,1,1,0,0,0] => 4
([2,1,1],6) => [2,1,1] => [1,0,1,1,0,1,0,0] => 4
([1,1,1,1],6) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 4
([5],6) => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
([4,1],6) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 5
([3,2],6) => [3,2] => [1,0,1,1,1,0,0,0] => 5
([3,1,1],6) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 5
([2,2,1],6) => [2,2,1] => [1,1,1,0,0,1,0,0] => 5
([2,1,1,1],6) => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 5
([1,1,1,1,1],6) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 5
([6,1],6) => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
([4,2],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 6
([5,1,1],6) => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 6
([3,3],6) => [3,3] => [1,1,1,0,1,0,0,0] => 6
([3,2,1],6) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 6
([4,1,1,1],6) => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 6
([2,2,2],6) => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
([2,2,1,1],6) => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 6
([3,1,1,1,1],6) => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 6
([2,1,1,1,1,1],6) => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 6
([7,2],6) => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 7
([6,1,1],6) => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
([4,3],6) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 7
([5,2,1],6) => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 7
([5,1,1,1],6) => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
([3,3,1],6) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 7
([3,2,2],6) => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 7
([4,2,1,1],6) => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 7
([4,1,1,1,1],6) => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7
([2,2,2,1],6) => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 7
([3,2,1,1,1],6) => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 7
([3,1,1,1,1,1],6) => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 7
([2,2,1,1,1,1,1],6) => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
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 area of the parallelogram polyomino associated with the Dyck path.
The (bivariate) generating function is given in [1].
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to bounded partition
Description
The (k-1)-bounded partition of a k-core.
Starting with a $k$-core, deleting all cells of hook length greater than or equal to $k$ yields a $(k-1)$-bounded partition [1, Theorem 7], see also [2, Section 1.2].