Identifier
Mp00154:
Graphs
—core⟶
Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Images
([],1) => ([],1) => [1] => [[1]]
([],2) => ([],1) => [1] => [[1]]
([(0,1)],2) => ([(0,1)],2) => [2] => [[1,2]]
([],3) => ([],1) => [1] => [[1]]
([(1,2)],3) => ([(0,1)],2) => [2] => [[1,2]]
([(0,2),(1,2)],3) => ([(0,1)],2) => [2] => [[1,2]]
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([],4) => ([],1) => [1] => [[1]]
([(2,3)],4) => ([(0,1)],2) => [2] => [[1,2]]
([(1,3),(2,3)],4) => ([(0,1)],2) => [2] => [[1,2]]
([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => [2] => [[1,2]]
([(0,3),(1,2)],4) => ([(0,1)],2) => [2] => [[1,2]]
([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => [2] => [[1,2]]
([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => [2] => [[1,2]]
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [[1,2,3,4]]
([],5) => ([],1) => [1] => [[1]]
([(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(2,4),(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(1,4),(2,3)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(0,1),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2) => [2] => [[1,2]]
([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [[1,2,3,4,5]]
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [[1,2,3,4]]
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [[1,2,3,4]]
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [[1,2,3,4]]
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [[1,2,3,4]]
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [[1,2,3,4,5]]
([],6) => ([],1) => [1] => [[1]]
([(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(2,5),(3,4)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,2),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,4),(2,3)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,2),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [[1,2,3,4,5]]
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => [2] => [[1,2]]
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => [3] => [[1,2,3]]
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [5] => [[1,2,3,4,5]]
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core
Description
The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
searching the database
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