Processing math: 100%

Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000713
Mp00166: Signed permutations even cycle typeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000713: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,1,1]
=> [1,1]
=> 5
[1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,2,3,-4] => [1,1,1]
=> [1,1]
=> 5
[1,2,-3,4] => [1,1,1]
=> [1,1]
=> 5
[1,-2,3,4] => [1,1,1]
=> [1,1]
=> 5
[-1,2,3,4] => [1,1,1]
=> [1,1]
=> 5
[1,2,4,3] => [2,1,1]
=> [1,1]
=> 5
[1,2,-4,-3] => [2,1,1]
=> [1,1]
=> 5
[1,3,2,4] => [2,1,1]
=> [1,1]
=> 5
[1,-3,-2,4] => [2,1,1]
=> [1,1]
=> 5
[1,4,3,2] => [2,1,1]
=> [1,1]
=> 5
[1,-4,3,-2] => [2,1,1]
=> [1,1]
=> 5
[2,1,3,4] => [2,1,1]
=> [1,1]
=> 5
[-2,-1,3,4] => [2,1,1]
=> [1,1]
=> 5
[2,1,4,3] => [2,2]
=> [2]
=> 10
[2,1,-4,-3] => [2,2]
=> [2]
=> 10
[-2,-1,4,3] => [2,2]
=> [2]
=> 10
[-2,-1,-4,-3] => [2,2]
=> [2]
=> 10
[3,2,1,4] => [2,1,1]
=> [1,1]
=> 5
[-3,2,-1,4] => [2,1,1]
=> [1,1]
=> 5
[3,4,1,2] => [2,2]
=> [2]
=> 10
[3,-4,1,-2] => [2,2]
=> [2]
=> 10
[-3,4,-1,2] => [2,2]
=> [2]
=> 10
[-3,-4,-1,-2] => [2,2]
=> [2]
=> 10
[4,2,3,1] => [2,1,1]
=> [1,1]
=> 5
[-4,2,3,-1] => [2,1,1]
=> [1,1]
=> 5
[4,3,2,1] => [2,2]
=> [2]
=> 10
[4,-3,-2,1] => [2,2]
=> [2]
=> 10
[-4,3,2,-1] => [2,2]
=> [2]
=> 10
[-4,-3,-2,-1] => [2,2]
=> [2]
=> 10
[1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 0
[1,2,3,4,-5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,2,3,-4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,2,3,-4,-5] => [1,1,1]
=> [1,1]
=> 5
[1,2,-3,4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,2,-3,4,-5] => [1,1,1]
=> [1,1]
=> 5
[1,2,-3,-4,5] => [1,1,1]
=> [1,1]
=> 5
[1,-2,3,4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[1,-2,3,4,-5] => [1,1,1]
=> [1,1]
=> 5
[1,-2,3,-4,5] => [1,1,1]
=> [1,1]
=> 5
[1,-2,-3,4,5] => [1,1,1]
=> [1,1]
=> 5
[-1,2,3,4,5] => [1,1,1,1]
=> [1,1,1]
=> 0
[-1,2,3,4,-5] => [1,1,1]
=> [1,1]
=> 5
[-1,2,3,-4,5] => [1,1,1]
=> [1,1]
=> 5
[-1,2,-3,4,5] => [1,1,1]
=> [1,1]
=> 5
[-1,-2,3,4,5] => [1,1,1]
=> [1,1]
=> 5
[1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 0
[1,2,3,5,-4] => [1,1,1]
=> [1,1]
=> 5
[1,2,3,-5,4] => [1,1,1]
=> [1,1]
=> 5
[1,2,3,-5,-4] => [2,1,1,1]
=> [1,1,1]
=> 0
Description
The dimension of the irreducible representation of Sp(4) labelled by an integer partition. Consider the symplectic group Sp(2n). Then the integer partition (μ1,,μk) of length at most n corresponds to the weight vector (μ1μ2,,μk2μk1,μn,0,,0). For example, the integer partition (2) labels the symmetric square of the vector representation, whereas the integer partition (1,1) labels the second fundamental representation.
Mp00166: Signed permutations even cycle typeInteger partitions
Mp00321: Integer partitions 2-conjugateInteger partitions
Mp00095: Integer partitions to binary wordBinary words
St001491: Binary words ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 12%
Values
[1,2,3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,3,4] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 0 - 3
[1,2,3,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,-3,4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,-2,3,4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-1,2,3,4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,4,3] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,2,-4,-3] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,3,2,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,-3,-2,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,4,3,2] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,-4,3,-2] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[2,1,3,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[-2,-1,3,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[2,1,4,3] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[2,1,-4,-3] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[-2,-1,4,3] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[-2,-1,-4,-3] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[3,2,1,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[-3,2,-1,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[3,4,1,2] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[3,-4,1,-2] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[-3,4,-1,2] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[-3,-4,-1,-2] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[4,2,3,1] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[-4,2,3,-1] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[4,3,2,1] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[4,-3,-2,1] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[-4,3,2,-1] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[-4,-3,-2,-1] => [2,2]
=> [4]
=> 10000 => ? = 10 - 3
[1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1,1]
=> 111110 => ? = 0 - 3
[1,2,3,4,-5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 0 - 3
[1,2,3,-4,5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 0 - 3
[1,2,3,-4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,-3,4,5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 0 - 3
[1,2,-3,4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,-3,-4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,-2,3,4,5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 0 - 3
[1,-2,3,4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,-2,3,-4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,-2,-3,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-1,2,3,4,5] => [1,1,1,1]
=> [1,1,1,1]
=> 11110 => ? = 0 - 3
[-1,2,3,4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-1,2,3,-4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-1,2,-3,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-1,-2,3,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,3,5,4] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 0 - 3
[1,2,3,5,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,3,-5,4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,3,-5,-4] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 0 - 3
[1,2,-3,5,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,2,-3,-5,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,-2,3,5,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,-2,3,-5,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[-1,2,3,5,4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[-1,2,3,-5,-4] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,2,4,3,5] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 0 - 3
[1,2,4,3,-5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,2,4,-3,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,-4,3,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,-4,-3,5] => [2,1,1,1]
=> [3,1,1]
=> 100110 => ? = 0 - 3
[1,2,-4,-3,-5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,-2,4,3,5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,-2,-4,-3,5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[-1,2,4,3,5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[-1,2,-4,-3,5] => [2,1,1]
=> [3,1]
=> 10010 => ? = 5 - 3
[1,2,4,5,3] => [3,1,1]
=> [2,1,1,1]
=> 101110 => ? = 5 - 3
[1,2,4,-5,-3] => [3,1,1]
=> [2,1,1,1]
=> 101110 => ? = 5 - 3
[1,2,-4,5,-3] => [3,1,1]
=> [2,1,1,1]
=> 101110 => ? = 5 - 3
[1,2,5,4,-3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,-5,4,3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,3,-2,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,-3,2,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,4,3,-2,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,-4,3,2,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,5,3,4,-2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,-5,3,4,2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[2,-1,3,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-2,1,3,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[3,2,-1,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-3,2,1,4,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[4,2,3,-1,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-4,2,3,1,5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[5,2,3,4,-1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-5,2,3,4,1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,3,6,4,-5] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,3,5,6,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,5,4,6,-3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,6,3,5,-4] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,2,4,6,5,-3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,5,3,4,6,-2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,4,3,6,5,-2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,6,2,4,5,-3] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[1,3,6,4,5,-2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[5,2,3,4,6,-1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[4,2,3,6,5,-1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[3,2,6,4,5,-1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[6,1,3,4,5,-2] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[2,6,3,4,5,-1] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
[-3,-2,1,4,5,6] => [1,1,1]
=> [1,1,1]
=> 1110 => 2 = 5 - 3
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let An=K[x]/(xn). We associate to a nonempty subset S of an (n-1)-set the module MS, which is the direct sum of An-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 MS. 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.
Mp00166: Signed permutations even cycle typeInteger partitions
Mp00042: Integer partitions initial tableauStandard tableaux
Mp00082: Standard tableaux to Gelfand-Tsetlin patternGelfand-Tsetlin patterns
St001713: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 12%
Values
[1,2,3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,3,4] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 0 - 5
[1,2,3,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,-3,4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,-2,3,4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-1,2,3,4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,4,3] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,-4,-3] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,3,2,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,-3,-2,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,4,3,2] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,-4,3,-2] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[2,1,3,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[-2,-1,3,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[2,1,4,3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[2,1,-4,-3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[-2,-1,4,3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[-2,-1,-4,-3] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[3,2,1,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[-3,2,-1,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[3,4,1,2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[3,-4,1,-2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[-3,4,-1,2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[-3,-4,-1,-2] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[4,2,3,1] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[-4,2,3,-1] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[4,3,2,1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[4,-3,-2,1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[-4,3,2,-1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[-4,-3,-2,-1] => [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 10 - 5
[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]]
=> ? = 0 - 5
[1,2,3,4,-5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 0 - 5
[1,2,3,-4,5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 0 - 5
[1,2,3,-4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,-3,4,5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 0 - 5
[1,2,-3,4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,-3,-4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,-2,3,4,5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 0 - 5
[1,-2,3,4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,-2,3,-4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,-2,-3,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-1,2,3,4,5] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 0 - 5
[-1,2,3,4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-1,2,3,-4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-1,2,-3,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-1,-2,3,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,3,5,4] => [2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 0 - 5
[1,2,3,5,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,3,-5,4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,3,-5,-4] => [2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 0 - 5
[1,2,-3,5,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,-3,-5,-4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,-2,3,5,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,-2,3,-5,-4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[-1,2,3,5,4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[-1,2,3,-5,-4] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,4,3,5] => [2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 0 - 5
[1,2,4,3,-5] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,4,-3,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,-4,3,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,-4,-3,5] => [2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 0 - 5
[1,2,-4,-3,-5] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,-2,4,3,5] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,-2,-4,-3,5] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[-1,2,4,3,5] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[-1,2,-4,-3,5] => [2,1,1]
=> [[1,2],[3],[4]]
=> [[2,1,1,0],[2,1,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,4,5,3] => [3,1,1]
=> [[1,2,3],[4],[5]]
=> [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,4,-5,-3] => [3,1,1]
=> [[1,2,3],[4],[5]]
=> [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,-4,5,-3] => [3,1,1]
=> [[1,2,3],[4],[5]]
=> [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
=> ? = 5 - 5
[1,2,5,4,-3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,-5,4,3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,3,-2,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,-3,2,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,4,3,-2,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,-4,3,2,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,5,3,4,-2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,-5,3,4,2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[2,-1,3,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-2,1,3,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[3,2,-1,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-3,2,1,4,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[4,2,3,-1,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-4,2,3,1,5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[5,2,3,4,-1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-5,2,3,4,1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,3,6,4,-5] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,3,5,6,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,5,4,6,-3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,6,3,5,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,2,4,6,5,-3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,5,3,4,6,-2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,4,3,6,5,-2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,6,2,4,5,-3] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[1,3,6,4,5,-2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[5,2,3,4,6,-1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[4,2,3,6,5,-1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[3,2,6,4,5,-1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[6,1,3,4,5,-2] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[2,6,3,4,5,-1] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
[-3,-2,1,4,5,6] => [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 0 = 5 - 5
Description
The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern.