Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000981
Mp00169: Signed permutations odd cycle typeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00230: Integer partitions parallelogram polyominoDyck paths
St000981: Dyck paths ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[-1,-2,-3] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[1,-2,-3,-4] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,2,-3,-4] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-2,3,-4] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-2,-3,4] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 4
[-1,-2,4,-3] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-2,-4,3] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,3,-2,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-3,2,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,4,-3,-2] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-4,-3,2] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[2,-1,-3,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-2,1,-3,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[2,-1,4,-3] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[2,-1,-4,3] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[-2,1,4,-3] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[-2,1,-4,3] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[3,-2,-1,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-3,-2,1,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[3,4,-1,-2] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[3,-4,-1,2] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[-3,4,1,-2] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[-3,-4,1,2] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[4,-2,-3,-1] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-4,-2,-3,1] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[4,3,-2,-1] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[4,-3,2,-1] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[-4,3,-2,1] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[-4,-3,2,1] => [2,2]
=> [2]
=> [1,0,1,0]
=> 4
[1,2,-3,-4,-5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[1,-2,3,-4,-5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[1,-2,-3,4,-5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[1,-2,-3,-4,5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 4
[-1,2,3,-4,-5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,2,-3,4,-5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,2,-3,-4,5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 4
[-1,-2,3,4,-5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-2,3,-4,5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 4
[-1,-2,-3,4,5] => [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 4
[-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 4
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 6
[1,-2,-3,5,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[1,-2,-3,-5,4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,2,-3,5,-4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
[-1,2,-3,-5,4] => [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 2
Description
The length of the longest zigzag subpath. This is the length of the longest consecutive subpath that is a zigzag of the form $010...$ or of the form $101...$.
Matching statistic: St001582
Mp00169: Signed permutations odd cycle typeInteger partitions
Mp00230: Integer partitions parallelogram polyominoDyck paths
Mp00201: Dyck paths RingelPermutations
St001582: Permutations ⟶ ℤResult quality: 17% values known / values provided: 17%distinct values known / distinct values provided: 33%
Values
[-1,-2,-3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[2,-1,4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[2,-1,-4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-2,1,4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-2,1,-4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[3,-2,-1,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-3,-2,1,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[3,4,-1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[3,-4,-1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-3,4,1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-3,-4,1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[4,-2,-3,-1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-4,-2,-3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[4,3,-2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[4,-3,2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-4,3,-2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-4,-3,2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,2,-3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,2,3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,-4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,-3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => ? = 6 - 1
[1,-2,-3,5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[1,-2,-3,-5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-3,5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-3,-5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,3,5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,3,-5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-3,5,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,5,-4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-3,-5,4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-3,-5,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,4,-3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[1,-2,-4,3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,4,-3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-4,3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,4,3,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,4,-3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,4,-3,-5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-4,3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-4,3,-5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-4,-3,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,4,5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,4,-5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-4,5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-4,-5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,5,3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,5,-3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-5,3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-5,-3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[1,-2,5,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[1,-2,-5,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,5,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-5,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,5,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,5,-4,3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,5,-4,-3] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-5,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-5,-4,-3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,3,2,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-3,-2,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,3,-2,5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,3,-2,-5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-3,2,5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-3,2,-5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-1,4,-3,2,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-4,-3,-2,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,4,5,-2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,4,-5,-2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-4,5,2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-4,-5,2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-1,5,-3,-4,2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-5,-3,-4,-2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,5,4,-3,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,5,-4,3,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-5,4,-3,2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Matching statistic: St001583
Mp00169: Signed permutations odd cycle typeInteger partitions
Mp00230: Integer partitions parallelogram polyominoDyck paths
Mp00201: Dyck paths RingelPermutations
St001583: Permutations ⟶ ℤResult quality: 17% values known / values provided: 17%distinct values known / distinct values provided: 33%
Values
[-1,-2,-3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,3,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[2,-1,4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[2,-1,-4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-2,1,4,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-2,1,-4,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[3,-2,-1,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-3,-2,1,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[3,4,-1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[3,-4,-1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-3,4,1,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-3,-4,1,2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[4,-2,-3,-1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-4,-2,-3,1] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[4,3,-2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[4,-3,2,-1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-4,3,-2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-4,-3,2,1] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,2,-3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,2,3,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,2,-3,-4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,3,4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,3,-4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,-3,4,5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 4 - 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => ? = 6 - 1
[1,-2,-3,5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[1,-2,-3,-5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-3,5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-3,-5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,3,5,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,3,-5,4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-3,5,4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,-3,5,-4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-3,-5,4] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-3,-5,-4] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,-2,4,-3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[1,-2,-4,3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,4,-3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-4,3,-5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,4,3,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,4,-3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,4,-3,-5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-4,3,5] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-4,3,-5] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-4,-3,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,4,5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,4,-5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-4,5,3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-4,-5,-3] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,5,3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,5,-3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-5,3,4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[-1,-2,-5,-3,-4] => [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 2 - 1
[1,-2,5,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[1,-2,-5,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,5,-4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,2,-5,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,5,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,5,-4,3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-2,5,-4,-3] => [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 4 - 1
[-1,-2,-5,4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 - 1
[-1,-2,-5,-4,-3] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,3,2,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-3,-2,-4,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,3,-2,5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,3,-2,-5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-3,2,5,-4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-3,2,-5,4] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-1,4,-3,2,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-4,-3,-2,-5] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,4,5,-2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,4,-5,-2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-4,5,2,-3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-4,-5,2,3] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[-1,5,-3,-4,2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[-1,-5,-3,-4,-2] => [1,1,1]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[1,5,4,-3,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,5,-4,3,-2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,-5,4,-3,2] => [2,2]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Matching statistic: St001603
Mp00260: Signed permutations Demazure product with inverseSigned permutations
Mp00166: Signed permutations even cycle typeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001603: Integer partitions ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 17%
Values
[-1,-2,-3] => [-1,-2,-3] => []
=> ?
=> ? = 2 - 3
[1,-2,-3,-4] => [1,-2,-3,-4] => [1]
=> []
=> ? = 2 - 3
[-1,2,-3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,-3,4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,-3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 4 - 3
[-1,-2,4,-3] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,-4,3] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,3,-2,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-3,2,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,4,-3,-2] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-4,-3,2] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[2,-1,-3,-4] => [-1,2,-3,-4] => [1]
=> []
=> ? = 2 - 3
[-2,1,-3,-4] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 3
[2,-1,4,-3] => [-1,2,-3,-4] => [1]
=> []
=> ? = 4 - 3
[2,-1,-4,3] => [-1,2,-3,-4] => [1]
=> []
=> ? = 4 - 3
[-2,1,4,-3] => [-2,-1,-3,4] => [2,1]
=> [1]
=> ? = 4 - 3
[-2,1,-4,3] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> ? = 4 - 3
[3,-2,-1,-4] => [-1,-2,3,-4] => [1]
=> []
=> ? = 2 - 3
[-3,-2,1,-4] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 3
[3,4,-1,-2] => [-1,-2,3,4] => [1,1]
=> [1]
=> ? = 4 - 3
[3,-4,-1,2] => [-1,-2,3,-4] => [1]
=> []
=> ? = 4 - 3
[-3,4,1,-2] => [-3,-2,-1,4] => [2,1]
=> [1]
=> ? = 4 - 3
[-3,-4,1,2] => [-3,-4,-1,-2] => [2,2]
=> [2]
=> ? = 4 - 3
[4,-2,-3,-1] => [-1,-2,-3,4] => [1]
=> []
=> ? = 2 - 3
[-4,-2,-3,1] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 3
[4,3,-2,-1] => [-1,-2,4,3] => [2]
=> []
=> ? = 4 - 3
[4,-3,2,-1] => [-1,-3,-2,4] => [2,1]
=> [1]
=> ? = 4 - 3
[-4,3,-2,1] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> ? = 4 - 3
[-4,-3,2,1] => [-3,-4,-1,-2] => [2,2]
=> [2]
=> ? = 4 - 3
[1,2,-3,-4,-5] => [1,2,-3,-4,-5] => [1,1]
=> [1]
=> ? = 2 - 3
[1,-2,3,-4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,-4,5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,-4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 4 - 3
[-1,2,3,-4,-5] => [-1,-2,3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[-1,2,-3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,2,-3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,2,-3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,-2,3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,-2,3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,-3,4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,-2,-3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,-3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,-3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 6 - 3
[1,-2,-3,5,-4] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,-5,4] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[-1,2,-3,5,-4] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,2,-3,-5,4] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[1,-3,2,-5,4] => [1,-3,-2,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[1,-4,-5,2,3] => [1,-4,-5,-2,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[1,-5,4,-3,2] => [1,-3,-2,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[1,-5,-4,3,2] => [1,-4,-5,-2,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,3,-5,4] => [-2,-1,3,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-4,3,5] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,4,-5,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-4,5,3] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-5,3,4] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-5,4,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-3,1,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,3,1,-5,4] => [-2,-1,3,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-4,-5,1,3] => [-4,2,-5,-1,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,4,-5,1,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-5,4,-3,1] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-5,-4,3,1] => [-4,2,-5,-1,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,5,-4,3,1] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,1,2,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,2,1,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-4,1,2,5] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,4,1,-5,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-4,1,5,2] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[3,-4,-5,2,1] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-4,5,2,1] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-5,1,2,4] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-5,1,4,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[3,-5,-4,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-5,4,1,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,1,-5,2,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,2,-5,1,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,3,-2,1,5] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-3,2,1,5] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[4,-3,2,-5,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,3,-2,5,1] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-3,2,5,1] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,3,-5,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-3,5,1,2] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[4,-5,1,-3,2] => [-5,-3,-2,4,-1] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-5,1,3,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,5,-2,1,3] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-5,2,1,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-5,3,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,1,4,-3,2] => [-5,-3,-2,4,-1] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,1,-4,3,2] => [-5,-4,3,-2,-1] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,2,4,-3,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,2,-4,3,1] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,3,-2,1,4] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,-3,2,1,4] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,3,-2,4,1] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,-3,2,4,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. Two colourings are considered equal, if they are obtained by an action of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001605
Mp00260: Signed permutations Demazure product with inverseSigned permutations
Mp00166: Signed permutations even cycle typeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001605: Integer partitions ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 17%
Values
[-1,-2,-3] => [-1,-2,-3] => []
=> ?
=> ? = 2 - 3
[1,-2,-3,-4] => [1,-2,-3,-4] => [1]
=> []
=> ? = 2 - 3
[-1,2,-3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,-3,4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,-3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 4 - 3
[-1,-2,4,-3] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-2,-4,3] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,3,-2,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-3,2,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,4,-3,-2] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[-1,-4,-3,2] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 3
[2,-1,-3,-4] => [-1,2,-3,-4] => [1]
=> []
=> ? = 2 - 3
[-2,1,-3,-4] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 3
[2,-1,4,-3] => [-1,2,-3,-4] => [1]
=> []
=> ? = 4 - 3
[2,-1,-4,3] => [-1,2,-3,-4] => [1]
=> []
=> ? = 4 - 3
[-2,1,4,-3] => [-2,-1,-3,4] => [2,1]
=> [1]
=> ? = 4 - 3
[-2,1,-4,3] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> ? = 4 - 3
[3,-2,-1,-4] => [-1,-2,3,-4] => [1]
=> []
=> ? = 2 - 3
[-3,-2,1,-4] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 3
[3,4,-1,-2] => [-1,-2,3,4] => [1,1]
=> [1]
=> ? = 4 - 3
[3,-4,-1,2] => [-1,-2,3,-4] => [1]
=> []
=> ? = 4 - 3
[-3,4,1,-2] => [-3,-2,-1,4] => [2,1]
=> [1]
=> ? = 4 - 3
[-3,-4,1,2] => [-3,-4,-1,-2] => [2,2]
=> [2]
=> ? = 4 - 3
[4,-2,-3,-1] => [-1,-2,-3,4] => [1]
=> []
=> ? = 2 - 3
[-4,-2,-3,1] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 3
[4,3,-2,-1] => [-1,-2,4,3] => [2]
=> []
=> ? = 4 - 3
[4,-3,2,-1] => [-1,-3,-2,4] => [2,1]
=> [1]
=> ? = 4 - 3
[-4,3,-2,1] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> ? = 4 - 3
[-4,-3,2,1] => [-3,-4,-1,-2] => [2,2]
=> [2]
=> ? = 4 - 3
[1,2,-3,-4,-5] => [1,2,-3,-4,-5] => [1,1]
=> [1]
=> ? = 2 - 3
[1,-2,3,-4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,-4,5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,-4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 4 - 3
[-1,2,3,-4,-5] => [-1,-2,3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[-1,2,-3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,2,-3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,2,-3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,-2,3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,-2,3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,-3,4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,-2,-3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,-3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 3
[-1,-2,-3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 6 - 3
[1,-2,-3,5,-4] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[1,-2,-3,-5,4] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 3
[-1,2,-3,5,-4] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[-1,2,-3,-5,4] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 3
[1,-3,2,-5,4] => [1,-3,-2,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[1,-4,-5,2,3] => [1,-4,-5,-2,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[1,-5,4,-3,2] => [1,-3,-2,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[1,-5,-4,3,2] => [1,-4,-5,-2,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,3,-5,4] => [-2,-1,3,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-4,3,5] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,4,-5,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-4,5,3] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-5,3,4] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,1,-5,4,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-3,1,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,3,1,-5,4] => [-2,-1,3,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-4,-5,1,3] => [-4,2,-5,-1,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,4,-5,1,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-5,4,-3,1] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[2,-5,-4,3,1] => [-4,2,-5,-1,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-2,5,-4,3,1] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,1,2,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,2,1,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-4,1,2,5] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,4,1,-5,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-4,1,5,2] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[3,-4,-5,2,1] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-4,5,2,1] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-5,1,2,4] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-5,1,4,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[3,-5,-4,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-3,-5,4,1,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,1,-5,2,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,2,-5,1,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,3,-2,1,5] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-3,2,1,5] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[4,-3,2,-5,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,3,-2,5,1] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-3,2,5,1] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,3,-5,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-3,5,1,2] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[4,-5,1,-3,2] => [-5,-3,-2,4,-1] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-5,1,3,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,5,-2,1,3] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-5,2,1,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-4,-5,3,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,1,4,-3,2] => [-5,-3,-2,4,-1] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,1,-4,3,2] => [-5,-4,3,-2,-1] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,2,4,-3,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,2,-4,3,1] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,3,-2,1,4] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,-3,2,1,4] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,3,-2,4,1] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
[-5,-3,2,4,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 1 = 4 - 3
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition. Two colourings are considered equal, if they are obtained by an action of the cyclic group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001604
Mp00260: Signed permutations Demazure product with inverseSigned permutations
Mp00166: Signed permutations even cycle typeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001604: Integer partitions ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 17%
Values
[-1,-2,-3] => [-1,-2,-3] => []
=> ?
=> ? = 2 - 4
[1,-2,-3,-4] => [1,-2,-3,-4] => [1]
=> []
=> ? = 2 - 4
[-1,2,-3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,-2,3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,-2,-3,4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,-2,-3,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 4 - 4
[-1,-2,4,-3] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,-2,-4,3] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,3,-2,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,-3,2,-4] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,4,-3,-2] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[-1,-4,-3,2] => [-1,-2,-3,-4] => []
=> ?
=> ? = 2 - 4
[2,-1,-3,-4] => [-1,2,-3,-4] => [1]
=> []
=> ? = 2 - 4
[-2,1,-3,-4] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 4
[2,-1,4,-3] => [-1,2,-3,-4] => [1]
=> []
=> ? = 4 - 4
[2,-1,-4,3] => [-1,2,-3,-4] => [1]
=> []
=> ? = 4 - 4
[-2,1,4,-3] => [-2,-1,-3,4] => [2,1]
=> [1]
=> ? = 4 - 4
[-2,1,-4,3] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> ? = 4 - 4
[3,-2,-1,-4] => [-1,-2,3,-4] => [1]
=> []
=> ? = 2 - 4
[-3,-2,1,-4] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 4
[3,4,-1,-2] => [-1,-2,3,4] => [1,1]
=> [1]
=> ? = 4 - 4
[3,-4,-1,2] => [-1,-2,3,-4] => [1]
=> []
=> ? = 4 - 4
[-3,4,1,-2] => [-3,-2,-1,4] => [2,1]
=> [1]
=> ? = 4 - 4
[-3,-4,1,2] => [-3,-4,-1,-2] => [2,2]
=> [2]
=> ? = 4 - 4
[4,-2,-3,-1] => [-1,-2,-3,4] => [1]
=> []
=> ? = 2 - 4
[-4,-2,-3,1] => [-2,-1,-3,-4] => [2]
=> []
=> ? = 2 - 4
[4,3,-2,-1] => [-1,-2,4,3] => [2]
=> []
=> ? = 4 - 4
[4,-3,2,-1] => [-1,-3,-2,4] => [2,1]
=> [1]
=> ? = 4 - 4
[-4,3,-2,1] => [-2,-1,-4,-3] => [2,2]
=> [2]
=> ? = 4 - 4
[-4,-3,2,1] => [-3,-4,-1,-2] => [2,2]
=> [2]
=> ? = 4 - 4
[1,2,-3,-4,-5] => [1,2,-3,-4,-5] => [1,1]
=> [1]
=> ? = 2 - 4
[1,-2,3,-4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 4
[1,-2,-3,4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 4
[1,-2,-3,-4,5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 4
[1,-2,-3,-4,-5] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 4 - 4
[-1,2,3,-4,-5] => [-1,-2,3,-4,-5] => [1]
=> []
=> ? = 2 - 4
[-1,2,-3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 4
[-1,2,-3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 4
[-1,2,-3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 4
[-1,-2,3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 4
[-1,-2,3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 4
[-1,-2,3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 4
[-1,-2,-3,4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 4
[-1,-2,-3,4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 4
[-1,-2,-3,-4,5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 4 - 4
[-1,-2,-3,-4,-5] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 6 - 4
[1,-2,-3,5,-4] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 4
[1,-2,-3,-5,4] => [1,-2,-3,-4,-5] => [1]
=> []
=> ? = 2 - 4
[-1,2,-3,5,-4] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 4
[-1,2,-3,-5,4] => [-1,-2,-3,-4,-5] => []
=> ?
=> ? = 2 - 4
[1,-3,2,-5,4] => [1,-3,-2,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[1,-4,-5,2,3] => [1,-4,-5,-2,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[1,-5,4,-3,2] => [1,-3,-2,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[1,-5,-4,3,2] => [1,-4,-5,-2,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,1,3,-5,4] => [-2,-1,3,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,1,-4,3,5] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,1,4,-5,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,1,-4,5,3] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,1,-5,3,4] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,1,-5,4,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[2,-3,1,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,3,1,-5,4] => [-2,-1,3,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[2,-4,-5,1,3] => [-4,2,-5,-1,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,4,-5,1,3] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[2,-5,4,-3,1] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[2,-5,-4,3,1] => [-4,2,-5,-1,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-2,5,-4,3,1] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,1,2,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,2,1,-5,4] => [-3,2,-1,-5,-4] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,-4,1,2,5] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,4,1,-5,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,-4,1,5,2] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[3,-4,-5,2,1] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,-4,5,2,1] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,-5,1,2,4] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,-5,1,4,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[3,-5,-4,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-3,-5,4,1,2] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,1,-5,2,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,2,-5,1,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,3,-2,1,5] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,-3,2,1,5] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[4,-3,2,-5,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,3,-2,5,1] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,-3,2,5,1] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,3,-5,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,-3,5,1,2] => [-3,-4,-1,-2,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[4,-5,1,-3,2] => [-5,-3,-2,4,-1] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,-5,1,3,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,5,-2,1,3] => [-2,-1,-4,-3,5] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,-5,2,1,3] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-4,-5,3,1,2] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,1,4,-3,2] => [-5,-3,-2,4,-1] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,1,-4,3,2] => [-5,-4,3,-2,-1] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,2,4,-3,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,2,-4,3,1] => [-4,-5,3,-1,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,3,-2,1,4] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,-3,2,1,4] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,3,-2,4,1] => [-2,-1,-5,4,-3] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
[-5,-3,2,4,1] => [-3,-5,-1,4,-2] => [2,2,1]
=> [2,1]
=> 0 = 4 - 4
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Mp00169: Signed permutations odd cycle typeInteger partitions
Mp00321: Integer partitions 2-conjugateInteger partitions
Mp00095: Integer partitions to binary wordBinary words
St001491: Binary words ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 17%
Values
[-1,-2,-3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[1,-2,-3,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,2,-3,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,3,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,-3,4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 4
[-1,-2,4,-3] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-2,-4,3] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,3,-2,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-3,2,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,4,-3,-2] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-4,-3,2] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[2,-1,-3,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-2,1,-3,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[2,-1,4,-3] => [2,2]
=> [4]
=> 10000 => ? = 4
[2,-1,-4,3] => [2,2]
=> [4]
=> 10000 => ? = 4
[-2,1,4,-3] => [2,2]
=> [4]
=> 10000 => ? = 4
[-2,1,-4,3] => [2,2]
=> [4]
=> 10000 => ? = 4
[3,-2,-1,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-3,-2,1,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[3,4,-1,-2] => [2,2]
=> [4]
=> 10000 => ? = 4
[3,-4,-1,2] => [2,2]
=> [4]
=> 10000 => ? = 4
[-3,4,1,-2] => [2,2]
=> [4]
=> 10000 => ? = 4
[-3,-4,1,2] => [2,2]
=> [4]
=> 10000 => ? = 4
[4,-2,-3,-1] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-4,-2,-3,1] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[4,3,-2,-1] => [2,2]
=> [4]
=> 10000 => ? = 4
[4,-3,2,-1] => [2,2]
=> [4]
=> 10000 => ? = 4
[-4,3,-2,1] => [2,2]
=> [4]
=> 10000 => ? = 4
[-4,-3,2,1] => [2,2]
=> [4]
=> 10000 => ? = 4
[1,2,-3,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[1,-2,3,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[1,-2,-3,4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[1,-2,-3,-4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[1,-2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 4
[-1,2,3,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,2,-3,4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,2,-3,-4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,2,-3,-4,-5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 4
[-1,-2,3,4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,3,-4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,3,-4,-5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 4
[-1,-2,-3,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,-3,4,-5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 4
[-1,-2,-3,-4,5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 4
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [1,1,1,1,1]
=> 111110 => ? = 6
[1,-2,-3,5,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[1,-2,-3,-5,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,2,-3,5,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,2,-3,-5,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-2,3,5,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-2,3,-5,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-2,-3,5,4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,-3,5,-4] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 4
[-1,-2,-3,-5,4] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 4
[-1,-2,-3,-5,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[1,-2,4,-3,-5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[1,-2,-4,3,-5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,2,4,-3,-5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,2,-4,3,-5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-2,4,3,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,4,-3,5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-2,4,-3,-5] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 4
[-1,-2,-4,3,5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 2
[-1,-2,-4,3,-5] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 4
[-1,-2,-4,-3,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,4,5,-3] => [3,1,1]
=> [2,1,1,1]
=> 101110 => ? = 2
[-1,-2,4,-5,3] => [3,1,1]
=> [2,1,1,1]
=> 101110 => ? = 2
[-1,-2,-4,5,3] => [3,1,1]
=> [2,1,1,1]
=> 101110 => ? = 2
[-1,-2,5,-4,3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-2,-5,-4,-3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,3,2,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-3,-2,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,4,-3,2,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-4,-3,-2,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,5,-3,-4,2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-1,-5,-3,-4,-2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[2,1,-3,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-2,-1,-3,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[3,-2,1,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-3,-2,-1,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[4,-2,-3,1,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-4,-2,-3,-1,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[5,-2,-3,-4,1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[-5,-2,-3,-4,-1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[7,-2,1,-4,3,-6,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
[6,-2,3,-4,-5,1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Mp00169: Signed permutations odd cycle typeInteger partitions
Mp00045: Integer partitions reading tableauStandard tableaux
Mp00082: Standard tableaux to Gelfand-Tsetlin patternGelfand-Tsetlin patterns
St001713: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 5% values known / values provided: 5%distinct values known / distinct values provided: 17%
Values
[-1,-2,-3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[1,-2,-3,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,2,-3,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,3,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,-3,4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,-3,-4] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,4,-3] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,-4,3] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,3,-2,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-3,2,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,4,-3,-2] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-4,-3,2] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[2,-1,-3,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-2,1,-3,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[2,-1,4,-3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[2,-1,-4,3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[-2,1,4,-3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[-2,1,-4,3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[3,-2,-1,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-3,-2,1,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[3,4,-1,-2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[3,-4,-1,2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[-3,4,1,-2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[-3,-4,1,2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[4,-2,-3,-1] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-4,-2,-3,1] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[4,3,-2,-1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[4,-3,2,-1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[-4,3,-2,1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[-4,-3,2,1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 4 - 2
[1,2,-3,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[1,-2,3,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[1,-2,-3,4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[1,-2,-3,-4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[1,-2,-3,-4,-5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,2,3,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,2,-3,4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,2,-3,-4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,2,-3,-4,-5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,3,4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,3,-4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,3,-4,-5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,-3,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,-3,4,-5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,-3,-4,5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 6 - 2
[1,-2,-3,5,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[1,-2,-3,-5,4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,2,-3,5,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,2,-3,-5,4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,3,5,-4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,3,-5,4] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,-3,5,4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,-3,5,-4] => [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,-3,-5,4] => [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,-3,-5,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[1,-2,4,-3,-5] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[1,-2,-4,3,-5] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,2,4,-3,-5] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,2,-4,3,-5] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,4,3,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,4,-3,5] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,4,-3,-5] => [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,-4,3,5] => [2,1,1]
=> [[1,4],[2],[3]]
=> [[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,-4,3,-5] => [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 4 - 2
[-1,-2,-4,-3,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,4,5,-3] => [3,1,1]
=> [[1,4,5],[2],[3]]
=> [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,4,-5,3] => [3,1,1]
=> [[1,4,5],[2],[3]]
=> [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,-4,5,3] => [3,1,1]
=> [[1,4,5],[2],[3]]
=> [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 - 2
[-1,-2,5,-4,3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-2,-5,-4,-3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,3,2,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-3,-2,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,4,-3,2,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-4,-3,-2,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,5,-3,-4,2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-1,-5,-3,-4,-2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[2,1,-3,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-2,-1,-3,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[3,-2,1,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-3,-2,-1,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[4,-2,-3,1,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-4,-2,-3,-1,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[5,-2,-3,-4,1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[-5,-2,-3,-4,-1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[7,-2,1,-4,3,-6,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
[6,-2,3,-4,-5,1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 2 - 2
Description
The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern.