Identifier
Mp00154:
Graphs
—core⟶
Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00045: Integer partitions —reading 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]]
>>> Load all 209 entries. <<<Map
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
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.
searching the database
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