Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Images
[1,0] => [1] => ([],1) => ([],1)
[1,0,1,0] => [2,1] => ([(0,1)],2) => ([(0,1)],2)
[1,1,0,0] => [1,2] => ([],2) => ([],1)
[1,0,1,0,1,0] => [2,3,1] => ([(0,2),(1,2)],3) => ([(0,1)],2)
[1,0,1,1,0,0] => [2,1,3] => ([(1,2)],3) => ([(0,1)],2)
[1,1,0,0,1,0] => [1,3,2] => ([(1,2)],3) => ([(0,1)],2)
[1,1,0,1,0,0] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2)
[1,1,1,0,0,0] => [1,2,3] => ([],3) => ([],1)
[1,0,1,0,1,0,1,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2)
[1,0,1,0,1,1,0,0] => [2,3,1,4] => ([(1,3),(2,3)],4) => ([(0,1)],2)
[1,0,1,1,0,0,1,0] => [2,1,4,3] => ([(0,3),(1,2)],4) => ([(0,1)],2)
[1,0,1,1,0,1,0,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,1)],2)
[1,0,1,1,1,0,0,0] => [2,1,3,4] => ([(2,3)],4) => ([(0,1)],2)
[1,1,0,0,1,0,1,0] => [1,3,4,2] => ([(1,3),(2,3)],4) => ([(0,1)],2)
[1,1,0,0,1,1,0,0] => [1,3,2,4] => ([(2,3)],4) => ([(0,1)],2)
[1,1,0,1,0,0,1,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => ([(0,1)],2)
[1,1,0,1,0,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2)
[1,1,0,1,1,0,0,0] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(0,1)],2)
[1,1,1,0,0,0,1,0] => [1,2,4,3] => ([(2,3)],4) => ([(0,1)],2)
[1,1,1,0,0,1,0,0] => [1,4,2,3] => ([(1,3),(2,3)],4) => ([(0,1)],2)
[1,1,1,0,1,0,0,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2)
[1,1,1,1,0,0,0,0] => [1,2,3,4] => ([],4) => ([],1)
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2)
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => ([(0,1)],2)
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,1)],2)
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => ([(0,1)],2)
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => ([(0,1)],2)
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => ([(0,1)],2)
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2)
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2)
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => ([(0,1)],2)
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,1)],2)
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => ([(3,4)],5) => ([(0,1)],2)
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => ([(0,1)],2)
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => ([(3,4)],5) => ([(0,1)],2)
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2)
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2)
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2)
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => ([(3,4)],5) => ([(0,1)],2)
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2)
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => ([(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2)
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2)
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => ([(3,4)],5) => ([(0,1)],2)
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => ([(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2)
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([],5) => ([],1)
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1)],2)
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1)],2)
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => ([(0,1)],2)
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => ([(0,1)],2)
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => ([(0,1)],2)
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2)
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2)
>>> Load all 197 entries. <<<Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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
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].
searching the database
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