Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001122
Mapping
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001122: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [[2,2],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => 1
[1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => 1
[1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => 1
[1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => 1
[1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => [1]
 => 1
[1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => 0
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 0
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => 0
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => 1
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => 1
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 0
[1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => 1
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => 1
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 0
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 0
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => 1
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 0
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 0
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 0
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => 0
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => 0
Description
The multiplicity of the sign representation in the Kronecker square corresponding to a partition. The Kronecker coefficient is the multiplicity $g_{\mu,\nu}^\lambda$ of the Specht module $S^\lambda$ in $S^\mu\otimes S^\nu$: $$ S^\mu\otimes S^\nu = \bigoplus_\lambda g_{\mu,\nu}^\lambda S^\lambda $$ This statistic records the Kronecker coefficient $g_{\lambda,\lambda}^{1^n}$, for $\lambda\vdash n$. It equals $1$ if and only if $\lambda$ is self-conjugate.
Matching statistic: St000260
(load all 2 compositions to match this statistic)
Mapping
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,1,0,0,1,0]
 => [2,1,3] => [3] => ([],3)
 => ? = 1 + 1
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? = 1 + 1
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [4] => ([],4)
 => ? = 0 + 1
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 1
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [4] => ([],4)
 => ? = 1 + 1
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [4] => ([],4)
 => ? = 1 + 1
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 1
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,4] => ([(3,4)],5)
 => ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,4] => ([(3,4)],5)
 => ? = 1 + 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [1,4] => ([(3,4)],5)
 => ? = 1 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [5] => ([],5)
 => ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [5] => ([],5)
 => ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [5] => ([],5)
 => ? = 1 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [5] => ([],5)
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,5,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,2,3,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,1,0,1,0,0,1,0,0]
 => [4,2,3,5,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,1,0,1,0,1,0,0,0]
 => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,1,1,0,0,1,0,0,0]
 => [5,3,2,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,2,4,3,6,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,2,4,5,6,3] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,2,5,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,5,4,6,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [1,5] => ([(4,5)],6)
 => ? = 0 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,3,2,4,6,5] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4,6] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,3,2,5,6,4] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,6,5,4] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,4,2,5,6] => [1,5] => ([(4,5)],6)
 => ? = 0 + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,4,2,6,5] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,3,4,5,2,6] => [1,5] => ([(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,3,4,5,6,2] => [1,5] => ([(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,3,4,6,5,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,3,5,4,2,6] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,3,5,4,6,2] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,3,6,4,5,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,4,3,6,5,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,6,3,4,5,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,6,4,3,5,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3,6,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [2,1,4,6,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [2,1,6,4,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,6,5,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [2,3,1,6,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,3,4,6,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,3,6,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,3,6,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,4,3,6,5,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,6,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,6,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,6,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,6,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,2,1,6,5,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,2,4,6,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,6,4,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,2,6,5,4,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [4,2,3,6,5,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [6,2,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,3,2,6,5,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [6,3,2,5,4,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [6,3,4,2,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [6,3,4,5,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [6,4,3,2,5,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [6,4,3,5,2,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,7,6,5,4,3] => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,7,6,5,4,1] => [3,2,1,1] => ([(0,5),(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)
 => 1 = 0 + 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [2,7,3,6,5,4,1] => [3,2,1,1] => ([(0,5),(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)
 => 1 = 0 + 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [2,7,4,6,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [2,7,6,4,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [3,2,7,6,5,4,1] => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [7,2,3,6,5,4,1] => [3,2,1,1] => ([(0,5),(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)
 => 1 = 0 + 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [7,2,4,6,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [7,2,6,4,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000259
(load all 2 compositions to match this statistic)
Mapping
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,1,0,0,1,0]
 => [2,1,3] => [3] => ([],3)
 => ? = 1 + 2
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? = 1 + 2
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [4] => ([],4)
 => ? = 0 + 2
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 2
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [4] => ([],4)
 => ? = 1 + 2
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [4] => ([],4)
 => ? = 1 + 2
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 2
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,4] => ([(3,4)],5)
 => ? = 0 + 2
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,4] => ([(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [1,4] => ([(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [5] => ([],5)
 => ? = 0 + 2
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [5] => ([],5)
 => ? = 0 + 2
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [5] => ([],5)
 => ? = 1 + 2
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [5] => ([],5)
 => ? = 1 + 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,5,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,0,1,0,0,0,1,0]
 => [4,2,3,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,1,0,1,0,0,1,0,0]
 => [4,2,3,5,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,1,0,1,0,1,0,0,0]
 => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,1,1,0,0,1,0,0,0]
 => [5,3,2,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 0 + 2
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,2,4,3,6,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,2,4,5,6,3] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,2,5,4,3,6] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,5,4,6,3] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [1,5] => ([(4,5)],6)
 => ? = 0 + 2
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,3,2,4,6,5] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4,6] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,3,2,5,6,4] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,6,5,4] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,4,2,5,6] => [1,5] => ([(4,5)],6)
 => ? = 0 + 2
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,4,2,6,5] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,3,4,5,2,6] => [1,5] => ([(4,5)],6)
 => ? = 1 + 2
[1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,3,4,5,6,2] => [1,5] => ([(4,5)],6)
 => ? = 1 + 2
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,3,4,6,5,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,3,5,4,2,6] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,3,5,4,6,2] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,3,6,4,5,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,4,3,6,5,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,6,3,4,5,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,6,4,3,5,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3,6,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [2,1,4,6,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [2,1,6,4,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,6,5,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [2,3,1,6,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,3,4,6,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,3,6,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,3,6,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,4,3,6,5,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,6,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,6,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,6,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,6,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,2,1,6,5,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,2,4,6,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,6,4,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,2,6,5,4,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [4,2,3,6,5,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [6,2,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,3,2,6,5,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [6,3,2,5,4,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [6,3,4,2,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [6,3,4,5,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [6,4,3,2,5,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [6,4,3,5,2,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,7,6,5,4,3] => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,7,6,5,4,1] => [3,2,1,1] => ([(0,5),(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)
 => 2 = 0 + 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [2,7,3,6,5,4,1] => [3,2,1,1] => ([(0,5),(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)
 => 2 = 0 + 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [2,7,4,6,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [2,7,6,4,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [3,2,7,6,5,4,1] => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [7,2,3,6,5,4,1] => [3,2,1,1] => ([(0,5),(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)
 => 2 = 0 + 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [7,2,4,6,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [7,2,6,4,5,3,1] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000264
(load all 2 compositions to match this statistic)
Mapping
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 50%
Values
[1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => [3] => ([],3)
 => ? = 1 + 3
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => [4] => ([],4)
 => ? = 1 + 3
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => [4] => ([],4)
 => ? = 0 + 3
[1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => [1,3] => ([(2,3)],4)
 => ? = 1 + 3
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [4] => ([],4)
 => ? = 1 + 3
[1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? = 1 + 3
[1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [4] => ([],4)
 => ? = 1 + 3
[1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 1 + 3
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5] => ([],5)
 => ? = 0 + 3
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,4] => ([(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 3
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [5] => ([],5)
 => ? = 0 + 3
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,4] => ([(3,4)],5)
 => ? = 0 + 3
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 0 + 3
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [5] => ([],5)
 => ? = 0 + 3
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4] => ([(3,4)],5)
 => ? = 1 + 3
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [5] => ([],5)
 => ? = 0 + 3
[1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,4] => ([(3,4)],5)
 => ? = 1 + 3
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [5] => ([],5)
 => ? = 1 + 3
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5] => ([],5)
 => ? = 0 + 3
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 3
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 0 + 3
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [6] => ([],6)
 => ? = 1 + 3
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [6] => ([],6)
 => ? = 0 + 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [6] => ([],6)
 => ? = 1 + 3
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [6] => ([],6)
 => ? = 1 + 3
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [6] => ([],6)
 => ? = 0 + 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => ? = 0 + 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [6] => ([],6)
 => ? = 1 + 3
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 3
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [6] => ([],6)
 => ? = 0 + 3
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,5] => ([(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [6] => ([],6)
 => ? = 1 + 3
[1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [6] => ([],6)
 => ? = 1 + 3
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 1 + 3
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,1,0,0]
 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 0 + 3
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [3,1,1,1] => ([(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)
 => 3 = 0 + 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 0 + 3
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.