Identifier
-
Mp00276:
Graphs
—to edge-partition of biconnected components⟶
Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001488: 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],[]] => 2
([(0,1),(0,2),(1,2)],3) => [3] => [[3],[]] => 2
([(2,3)],4) => [1] => [[1],[]] => 1
([(1,3),(2,3)],4) => [1,1] => [[1,1],[]] => 2
([(0,3),(1,3),(2,3)],4) => [1,1,1] => [[1,1,1],[]] => 2
([(0,3),(1,2)],4) => [1,1] => [[1,1],[]] => 2
([(0,3),(1,2),(2,3)],4) => [1,1,1] => [[1,1,1],[]] => 2
([(1,2),(1,3),(2,3)],4) => [3] => [[3],[]] => 2
([(0,3),(1,2),(1,3),(2,3)],4) => [3,1] => [[3,1],[]] => 3
([(0,2),(0,3),(1,2),(1,3)],4) => [4] => [[4],[]] => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [5] => [[5],[]] => 2
([(3,4)],5) => [1] => [[1],[]] => 1
([(2,4),(3,4)],5) => [1,1] => [[1,1],[]] => 2
([(1,4),(2,4),(3,4)],5) => [1,1,1] => [[1,1,1],[]] => 2
([(0,4),(1,4),(2,4),(3,4)],5) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(1,4),(2,3)],5) => [1,1] => [[1,1],[]] => 2
([(1,4),(2,3),(3,4)],5) => [1,1,1] => [[1,1,1],[]] => 2
([(0,1),(2,4),(3,4)],5) => [1,1,1] => [[1,1,1],[]] => 2
([(2,3),(2,4),(3,4)],5) => [3] => [[3],[]] => 2
([(0,4),(1,4),(2,3),(3,4)],5) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(1,4),(2,3),(2,4),(3,4)],5) => [3,1] => [[3,1],[]] => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [3,1,1] => [[3,1,1],[]] => 3
([(1,3),(1,4),(2,3),(2,4)],5) => [4] => [[4],[]] => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [4,1] => [[4,1],[]] => 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [[5],[]] => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,1,1] => [[3,1,1],[]] => 3
([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(0,1),(2,3),(2,4),(3,4)],5) => [3,1] => [[3,1],[]] => 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [3,1,1] => [[3,1,1],[]] => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [[5],[]] => 2
([(4,5)],6) => [1] => [[1],[]] => 1
([(3,5),(4,5)],6) => [1,1] => [[1,1],[]] => 2
([(2,5),(3,5),(4,5)],6) => [1,1,1] => [[1,1,1],[]] => 2
([(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(2,5),(3,4)],6) => [1,1] => [[1,1],[]] => 2
([(2,5),(3,4),(4,5)],6) => [1,1,1] => [[1,1,1],[]] => 2
([(1,2),(3,5),(4,5)],6) => [1,1,1] => [[1,1,1],[]] => 2
([(3,4),(3,5),(4,5)],6) => [3] => [[3],[]] => 2
([(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(0,1),(2,5),(3,5),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(2,5),(3,4),(3,5),(4,5)],6) => [3,1] => [[3,1],[]] => 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 3
([(2,4),(2,5),(3,4),(3,5)],6) => [4] => [[4],[]] => 2
([(0,5),(1,5),(2,4),(3,4)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,1] => [[4,1],[]] => 3
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5] => [[5],[]] => 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(0,5),(1,4),(2,3)],6) => [1,1,1] => [[1,1,1],[]] => 2
([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(0,1),(2,5),(3,4),(4,5)],6) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(1,2),(3,4),(3,5),(4,5)],6) => [3,1] => [[3,1],[]] => 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 3
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [3,1,1] => [[3,1,1],[]] => 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [5] => [[5],[]] => 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [4,1] => [[4,1],[]] => 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,1,1] => [[3,1,1],[]] => 3
([(5,6)],7) => [1] => [[1],[]] => 1
([(4,6),(5,6)],7) => [1,1] => [[1,1],[]] => 2
([(3,6),(4,6),(5,6)],7) => [1,1,1] => [[1,1,1],[]] => 2
([(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(3,6),(4,5)],7) => [1,1] => [[1,1],[]] => 2
([(3,6),(4,5),(5,6)],7) => [1,1,1] => [[1,1,1],[]] => 2
([(2,3),(4,6),(5,6)],7) => [1,1,1] => [[1,1,1],[]] => 2
([(4,5),(4,6),(5,6)],7) => [3] => [[3],[]] => 2
([(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(1,2),(3,6),(4,6),(5,6)],7) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(3,6),(4,5),(4,6),(5,6)],7) => [3,1] => [[3,1],[]] => 3
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1] => [[3,1,1],[]] => 3
([(3,5),(3,6),(4,5),(4,6)],7) => [4] => [[4],[]] => 2
([(1,6),(2,6),(3,5),(4,5)],7) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [4,1] => [[4,1],[]] => 3
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5] => [[5],[]] => 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,1,1] => [[3,1,1],[]] => 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(1,6),(2,5),(3,4)],7) => [1,1,1] => [[1,1,1],[]] => 2
([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(1,2),(3,6),(4,5),(5,6)],7) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(0,3),(1,2),(4,6),(5,6)],7) => [1,1,1,1] => [[1,1,1,1],[]] => 2
([(2,3),(4,5),(4,6),(5,6)],7) => [3,1] => [[3,1],[]] => 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,1,1] => [[3,1,1],[]] => 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [3,1,1] => [[3,1,1],[]] => 3
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [5] => [[5],[]] => 2
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,1] => [[4,1],[]] => 3
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,1,1] => [[3,1,1],[]] => 3
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searching the database for the individual values of this statistic
Description
The number of corners of a skew partition.
This is also known as the number of removable cells of the skew partition.
This is also known as the number of removable cells 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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