Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000508
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000508: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],3)
 => [1,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([],4)
 => [1,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => [[1,2]]
 => 4
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 0
([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => [[1,3],[2]]
 => 0
([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => [[1,2]]
 => 4
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => [[1,2]]
 => 4
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 0
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [[1,4],[2],[3]]
 => 2
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => [[1,3],[2]]
 => 0
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [[1,2]]
 => 4
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => [3,3]
 => [3]
 => [[1,2,3]]
 => 9
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [2,2]
 => [[1,2],[3,4]]
 => 4
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [[1,2]]
 => 4
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => [[1,3],[2]]
 => 0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [[1,2]]
 => 4
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2]
 => [2]
 => [[1,2]]
 => 4
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,3]
 => [3]
 => [[1,2,3]]
 => 9
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [[1,2]]
 => 4
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => [[1,2,3]]
 => 9
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [[1,2]]
 => 4
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => 0
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => 1
([(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 0
([(3,6),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(3,6),(4,5)],7)
 => [2,2,1,1,1]
 => [2,1,1,1]
 => [[1,5],[2],[3],[4]]
 => 0
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [2,1,1]
 => [[1,4],[2],[3]]
 => 2
([(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 0
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(1,2),(3,6),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => [[1,3],[2]]
 => 0
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [5,2]
 => [2]
 => [[1,2]]
 => 4
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => [[1],[2]]
 => 0
([(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => [[1],[2],[3]]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [3,3,1]
 => [3,1]
 => [[1,3,4],[2]]
 => 0
Description
Eigenvalues of the random-to-random operator acting on a simple module. The simple module of the symmetric group indexed by a partition λ has dimension equal to the number of standard tableaux of shape λ. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape λ; this statistic gives all the eigenvalues of the operator acting on the module [1].