Identifier
Values
[1,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[2,2] => [2] => [1,0,1,0] => [2,1] => 1
[2,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[3,2] => [2] => [1,0,1,0] => [2,1] => 1
[3,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[2,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[4,2] => [2] => [1,0,1,0] => [2,1] => 1
[4,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[3,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[3,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[2,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[5,2] => [2] => [1,0,1,0] => [2,1] => 1
[5,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[4,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[4,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[3,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[6,2] => [2] => [1,0,1,0] => [2,1] => 1
[6,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[5,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[5,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[4,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[4,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[7,2] => [2] => [1,0,1,0] => [2,1] => 1
[7,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[6,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[6,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[5,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[5,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[8,2] => [2] => [1,0,1,0] => [2,1] => 1
[8,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[7,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[7,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[7,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[6,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[6,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[9,2] => [2] => [1,0,1,0] => [2,1] => 1
[9,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[8,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[8,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[8,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[7,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[7,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[7,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[10,2] => [2] => [1,0,1,0] => [2,1] => 1
[10,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[9,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[9,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[9,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[8,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[8,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[8,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[8,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[7,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[7,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[11,2] => [2] => [1,0,1,0] => [2,1] => 1
[11,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[10,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[10,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[10,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
>>> Load all 166 entries. <<<
[9,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[9,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[9,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[9,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[8,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[8,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[7,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[7,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[12,2] => [2] => [1,0,1,0] => [2,1] => 1
[12,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[11,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[11,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[11,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[10,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[10,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[10,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[10,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[9,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[9,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[8,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[8,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[13,2] => [2] => [1,0,1,0] => [2,1] => 1
[13,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[12,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[12,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[12,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[11,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[11,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[11,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[11,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[10,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[10,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[9,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[9,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[14,2] => [2] => [1,0,1,0] => [2,1] => 1
[14,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[13,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[13,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[13,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[12,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[12,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[12,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[12,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[11,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[11,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[10,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[10,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[15,2] => [2] => [1,0,1,0] => [2,1] => 1
[15,1,1] => [1,1] => [1,1,0,0] => [1,2] => 0
[14,3] => [3] => [1,0,1,0,1,0] => [2,1,3] => 1
[14,2,1] => [2,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[14,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => [1,3,2] => 1
[13,4] => [4] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => 1
[13,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => 2
[13,2,2] => [2,2] => [1,1,1,0,0,0] => [1,2,3] => 0
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => 2
[13,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 1
[12,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[12,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[11,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 1
[11,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
search for individual values
searching the database for the individual values of this statistic
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
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 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
first row removal
Description
Removes the first entry of an integer partition