Identifier
Values
([],1) => [1] => [[1]] => 1
([],2) => [2] => [[1,2]] => 2
([(0,1)],2) => [1] => [[1]] => 1
([],3) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(1,2)],3) => [3] => [[1,2,3]] => 3
([(0,1),(0,2)],3) => [2] => [[1,2]] => 2
([(0,2),(2,1)],3) => [1] => [[1]] => 1
([(0,2),(1,2)],3) => [2] => [[1,2]] => 2
([(0,1),(0,2),(0,3)],4) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,2),(0,3),(3,1)],4) => [3] => [[1,2,3]] => 3
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => [[1,2]] => 2
([(1,2),(2,3)],4) => [4] => [[1,2,3,4]] => 4
([(0,3),(3,1),(3,2)],4) => [2] => [[1,2]] => 2
([(0,3),(1,3),(3,2)],4) => [2] => [[1,2]] => 2
([(0,3),(1,3),(2,3)],4) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,3),(1,2)],4) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,3),(1,2),(1,3)],4) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => [[1,2],[3,4]] => 1
([(0,3),(2,1),(3,2)],4) => [1] => [[1]] => 1
([(0,3),(1,2),(2,3)],4) => [3] => [[1,2,3]] => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => [[1,2]] => 2
([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(4,1),(4,2),(4,3)],5) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => [[1,2]] => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [6] => [[1,2,3,4,5,6]] => 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(1,2),(1,4),(4,3)],5) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,2),(0,4),(3,1),(4,3)],5) => [4] => [[1,2,3,4]] => 4
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => [[1,2,3]] => 3
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [6] => [[1,2,3,4,5,6]] => 6
([(1,4),(3,2),(4,3)],5) => [5] => [[1,2,3,4,5]] => 5
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => [[1,2]] => 2
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => [[1,2,3]] => 3
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => [[1,2,3]] => 3
([(0,4),(1,2),(2,3),(2,4)],5) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => [[1]] => 1
([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,4),(1,2),(2,3),(3,4)],5) => [4] => [[1,2,3,4]] => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => [[1,2]] => 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => [[1,2],[3,4]] => 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [6] => [[1,2,3,4,5,6]] => 6
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => [[1,2],[3,4]] => 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [6] => [[1,2,3,4,5,6]] => 6
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => [[1,2],[3,4]] => 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => [[1,2]] => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [6] => [[1,2,3,4,5,6]] => 6
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => [[1,2,3]] => 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [4] => [[1,2,3,4]] => 4
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => [[1,2]] => 2
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [6] => [[1,2,3,4,5,6]] => 6
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [6] => [[1,2,3,4,5,6]] => 6
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => [5] => [[1,2,3,4,5]] => 5
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => [6] => [[1,2,3,4,5,6]] => 6
([(1,5),(3,4),(4,2),(5,3)],6) => [6] => [[1,2,3,4,5,6]] => 6
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [2] => [[1,2]] => 2
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => [4] => [[1,2,3,4]] => 4
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [2] => [[1,2]] => 2
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => [[1,2,3,4]] => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [3] => [[1,2,3]] => 3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => [[1]] => 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => [[1,2,3]] => 3
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => [[1,2,3,4,5]] => 5
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [2] => [[1,2]] => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [3] => [[1,2,3]] => 3
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => [[1,2,3,4,5]] => 5
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [2] => [[1,2]] => 2
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => [[1,2]] => 2
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => [6] => [[1,2,3,4,5,6]] => 6
>>> Load all 151 entries. <<<
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [4] => [[1,2,3,4]] => 4
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [2] => [[1,2]] => 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => [3,3] => [[1,2,3],[4,5,6]] => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [3] => [[1,2,3]] => 3
([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => [5] => [[1,2,3,4,5]] => 5
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [3] => [[1,2,3]] => 3
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [2,2] => [[1,2],[3,4]] => 1
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [3,2] => [[1,2,5],[3,4]] => 1
([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [2] => [[1,2]] => 2
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => [4] => [[1,2,3,4]] => 4
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => [5] => [[1,2,3,4,5]] => 5
([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) => [7] => [[1,2,3,4,5,6,7]] => 7
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [3] => [[1,2,3]] => 3
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => [[1]] => 1
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => [[1,2,3]] => 3
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [3] => [[1,2,3]] => 3
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [4,2] => [[1,2,5,6],[3,4]] => 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [2] => [[1,2]] => 2
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => [[1,2,3,4]] => 4
([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => [[1,2,3,4,5,6]] => 6
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [2] => [[1,2]] => 2
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [4] => [[1,2,3,4]] => 4
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [3,2] => [[1,2,5],[3,4]] => 1
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Description
Eigenvalues of the top-to-random operator acting on a simple module.
These eigenvalues are given in [1] and [3].
The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module.
This statistic bears different names, such as the type in [2] or eig in [3].
Similarly, the eigenvalues of the random-to-random operator acting on a simple module is St000508Eigenvalues of the random-to-random operator acting on a simple module..
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.