Identifier
Values
[[1,2,3]] => [1,2,3] => [1,2] => [1,0,1,0] => 2
[[1,2],[3]] => [3,1,2] => [1,2] => [1,0,1,0] => 2
[[1,2,3,4]] => [1,2,3,4] => [1,2,3] => [1,0,1,0,1,0] => 3
[[1,3,4],[2]] => [2,1,3,4] => [2,1,3] => [1,1,0,0,1,0] => 2
[[1,2,3],[4]] => [4,1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 3
[[1,3],[2,4]] => [2,4,1,3] => [2,1,3] => [1,1,0,0,1,0] => 2
[[1,3],[2],[4]] => [4,2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 2
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[[1,2,4,5],[3]] => [3,1,2,4,5] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 2
[[1,2,3,4],[5]] => [5,1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[[1,3,5],[2,4]] => [2,4,1,3,5] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 2
[[1,2,5],[3,4]] => [3,4,1,2,5] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 2
[[1,3,4],[2,5]] => [2,5,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[[1,2,4],[3,5]] => [3,5,1,2,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 2
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 2
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 2
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 2
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 2
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 2
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 2
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 3
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 3
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 3
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 3
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 2
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 2
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 2
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 3
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 3
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 2
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 2
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 2
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 2
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 2
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 2
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 3
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 3
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 2
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 2
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 2
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 2
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 2
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 2
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 2
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 2
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 2
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.