Processing math: 100%

Identifier
Values
[1] => [1,0] => [[1]] => [[1]] => 1
[2] => [1,0,1,0] => [[1,0],[0,1]] => [[1,1],[2]] => 4
[1,1] => [1,1,0,0] => [[0,1],[1,0]] => [[1,2],[2]] => 5
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 sum of the entries of a semistandard tableau.
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 semistandard tableau via monotone triangles
Description
The semistandard tableau corresponding the monotone triangle of an alternating sign matrix.
This is obtained by interpreting each row of the monotone triangle as an integer partition, and filling the cells of the smallest partition with ones, the second smallest with twos, and so on.
Map
to symmetric ASM
Description
The diagonally symmetric alternating sign matrix corresponding to a Dyck path.