Identifier
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Images
[1,0] => [2,1] => ([(0,1)],2) => [2]
[1,0,1,0] => [3,1,2] => ([(0,2),(1,2)],3) => [3]
[1,1,0,0] => [2,3,1] => ([(0,2),(1,2)],3) => [3]
[1,0,1,0,1,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => [4]
[1,0,1,1,0,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => [4]
[1,1,0,0,1,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => [4]
[1,1,0,1,0,0] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4]
[1,1,1,0,0,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => [4]
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5]
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => [5]
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5]
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => [5]
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5]
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5]
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => [5]
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => [5]
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => [5]
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => [5]
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5]
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6]
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [6]
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [6]
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [6]
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => [6]
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [6]
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [6]
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [6]
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => [6]
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => [6]
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => [6]
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [6]
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [6]
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [6]
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [6]
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [6]
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [6]
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6]
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [6]
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6]
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [7]
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [7]
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => ([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [7]
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [7]
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [7]
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [7]
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => ([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [7]
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => ([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [7]
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => ([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => ([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [7]
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => ([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7]
>>> Load all 271 entries. <<<Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
searching the database
Sorry, this map was not found in the database.