Identifier
-
Mp00175:
Permutations
—inverse Foata bijection⟶
Permutations
Mp00209: Permutations —pattern poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001812: Graphs ⟶ ℤ
Values
[1] => [1] => ([],1) => ([],1) => 0
[1,2] => [1,2] => ([(0,1)],2) => ([],2) => 0
[2,1] => [2,1] => ([(0,1)],2) => ([],2) => 0
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => ([],3) => 0
[1,3,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[2,1,3] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[3,2,1] => [3,2,1] => ([(0,2),(2,1)],3) => ([],3) => 0
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[1,2,4,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[1,3,4,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
[1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[2,1,3,4] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[2,3,4,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[3,2,1,4] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[3,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[4,1,2,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[4,2,1,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
[4,3,1,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[5,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The biclique partition number of a graph.
The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph $K_n$ has biclique partition number $n - 1$.
The biclique partition number of a graph is the minimum number of pairwise edge disjoint complete bipartite subgraphs so that each edge belongs to exactly one of them. A theorem of Graham and Pollak [1] asserts that the complete graph $K_n$ has biclique partition number $n - 1$.
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!