Identifier
-
Mp00276:
Graphs
—to edge-partition of biconnected components⟶
Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001597: Skew partitions ⟶ ℤ
Values
([(0,1)],2) => [1] => [[1],[]] => 1
([(1,2)],3) => [1] => [[1],[]] => 1
([(0,2),(1,2)],3) => [1,1] => [[1,1],[]] => 1
([(0,1),(0,2),(1,2)],3) => [3] => [[3],[]] => 1
([(2,3)],4) => [1] => [[1],[]] => 1
([(1,3),(2,3)],4) => [1,1] => [[1,1],[]] => 1
([(0,3),(1,3),(2,3)],4) => [1,1,1] => [[1,1,1],[]] => 1
([(0,3),(1,2)],4) => [1,1] => [[1,1],[]] => 1
([(0,3),(1,2),(2,3)],4) => [1,1,1] => [[1,1,1],[]] => 1
([(1,2),(1,3),(2,3)],4) => [3] => [[3],[]] => 1
([(0,3),(1,2),(1,3),(2,3)],4) => [3,1] => [[3,1],[]] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [4] => [[4],[]] => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [5] => [[5],[]] => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [6] => [[6],[]] => 1
([(3,4)],5) => [1] => [[1],[]] => 1
([(2,4),(3,4)],5) => [1,1] => [[1,1],[]] => 1
([(1,4),(2,4),(3,4)],5) => [1,1,1] => [[1,1,1],[]] => 1
([(0,4),(1,4),(2,4),(3,4)],5) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(1,4),(2,3)],5) => [1,1] => [[1,1],[]] => 1
([(1,4),(2,3),(3,4)],5) => [1,1,1] => [[1,1,1],[]] => 1
([(0,1),(2,4),(3,4)],5) => [1,1,1] => [[1,1,1],[]] => 1
([(2,3),(2,4),(3,4)],5) => [3] => [[3],[]] => 1
([(0,4),(1,4),(2,3),(3,4)],5) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(1,4),(2,3),(2,4),(3,4)],5) => [3,1] => [[3,1],[]] => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [3,1,1] => [[3,1,1],[]] => 1
([(1,3),(1,4),(2,3),(2,4)],5) => [4] => [[4],[]] => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [4,1] => [[4,1],[]] => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [[5],[]] => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,1,1] => [[3,1,1],[]] => 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5,1] => [[5,1],[]] => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [6] => [[6],[]] => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [7] => [[7],[]] => 1
([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => [[3,1],[]] => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [3,1,1] => [[3,1,1],[]] => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => [3,3] => [[3,3],[]] => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [[5],[]] => 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [6] => [[6],[]] => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => [7] => [[7],[]] => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => [5,1] => [[5,1],[]] => 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [6] => [[6],[]] => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [6,1] => [[6,1],[]] => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => [7] => [[7],[]] => 1
([(4,5)],6) => [1] => [[1],[]] => 1
([(3,5),(4,5)],6) => [1,1] => [[1,1],[]] => 1
([(2,5),(3,5),(4,5)],6) => [1,1,1] => [[1,1,1],[]] => 1
([(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
([(2,5),(3,4)],6) => [1,1] => [[1,1],[]] => 1
([(2,5),(3,4),(4,5)],6) => [1,1,1] => [[1,1,1],[]] => 1
([(1,2),(3,5),(4,5)],6) => [1,1,1] => [[1,1,1],[]] => 1
([(3,4),(3,5),(4,5)],6) => [3] => [[3],[]] => 1
([(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(0,1),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(2,5),(3,4),(3,5),(4,5)],6) => [3,1] => [[3,1],[]] => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [[3,1,1,1],[]] => 1
([(2,4),(2,5),(3,4),(3,5)],6) => [4] => [[4],[]] => 1
([(0,5),(1,5),(2,4),(3,4)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,1] => [[4,1],[]] => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5] => [[5],[]] => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,1,1] => [[4,1,1],[]] => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => [[5,1],[]] => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [[3,1,1,1],[]] => 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1,1] => [[5,1,1],[]] => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6] => [[6],[]] => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [4,1,1] => [[4,1,1],[]] => 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6,1] => [[6,1],[]] => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [7] => [[7],[]] => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1,1] => [[5,1,1],[]] => 1
([(0,5),(1,4),(2,3)],6) => [1,1,1] => [[1,1,1],[]] => 1
([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(0,1),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 1
([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => [[3,1],[]] => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => [[3,1,1,1],[]] => 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3] => [[3,3],[]] => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,1] => [[3,3,1],[]] => 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [5] => [[5],[]] => 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [4,1,1] => [[4,1,1],[]] => 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [6] => [[6],[]] => 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [5,1] => [[5,1],[]] => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [5,1] => [[5,1],[]] => 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [[3,1,1,1],[]] => 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [6,1] => [[6,1],[]] => 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1,1] => [[5,1,1],[]] => 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [7] => [[7],[]] => 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => [[4,1],[]] => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,1,1] => [[3,1,1],[]] => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [4,1,1] => [[4,1,1],[]] => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => [3,1,1,1] => [[3,1,1,1],[]] => 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [[3,1,1,1],[]] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => [[5,1],[]] => 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => [[3,1,1,1],[]] => 1
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Description
The Frobenius rank of a skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
Map
to edge-partition of biconnected components
Description
Sends a graph to the partition recording the number of edges in its biconnected components.
The biconnected components are also known as blocks of a graph.
The biconnected components are also known as blocks of a graph.
Map
to skew partition
Description
The partition regarded as a skew partition.
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