searching the database
Your data matches 90 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000920
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St000920: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St000920: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1,1,0,0]
=> [1,1,0,0]
=> [1,1,0,0]
=> 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> 1
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> 2
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 1
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> 2
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 2
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [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
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> 2
Description
The logarithmic height of a Dyck path.
This is the floor of the binary logarithm of the usual height increased by one:
$$
\lfloor\log_2(1+height(D))\rfloor
$$
Matching statistic: St001198
(load all 46 compositions to match this statistic)
(load all 46 compositions to match this statistic)
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 80%●distinct values known / distinct values provided: 33%
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 80%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [1] => [1] => [1,0]
=> ? = 1
[1,0,1,0]
=> [1,2] => [1,2] => [1,0,1,0]
=> 2
[1,1,0,0]
=> [2,1] => [2,1] => [1,1,0,0]
=> ? = 1
[1,0,1,0,1,0]
=> [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,0]
=> [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,0]
=> [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,0]
=> [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
=> ? ∊ {1,1}
[1,1,1,0,0,0]
=> [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? ∊ {1,1}
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,1,0,1,1,0,0,0]
=> [2,4,3,1] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,1,1,0,0,0,1,0]
=> [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [3,2,4,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,1,1,0,1,0,0,0]
=> [4,2,3,1] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,0,0,1,0,1,0]
=> [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [3,2,4,1,5] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,1,0,0,0,1,0]
=> [4,2,3,1,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,1,0,1,0,0,0]
=> [5,2,3,4,1] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,1,1,0,0,0,0,1,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,1,0,0,1,0,0,0]
=> [5,3,2,4,1] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [5,3,4,2,1] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,1,1,1,0,0,0,0,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,5,1] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,5,4,6,1] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,5,4,1] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,3,5,6,1] => [6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,3,6,5,1] => [6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,5,3,4,6,1] => [6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,5,4,3,6,1] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,5,4,3,1] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,2,4,5,6,1] => [6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,2,4,6,5,1] => [6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,5,4,6,1] => [6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,2,6,5,4,1] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,2,3,5,6,1] => [6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,2,3,6,5,1] => [6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,2,3,4,6,1] => [6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,4,3,6,1] => [6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,3,2,5,6,1] => [6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,3,2,6,5,1] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,2,4,6,1] => [6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,3,4,2,6,1] => [6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,4,3,2,6,1] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
Description
The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001206
(load all 46 compositions to match this statistic)
(load all 46 compositions to match this statistic)
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 80%●distinct values known / distinct values provided: 33%
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 80%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [1] => [1] => [1,0]
=> ? = 1
[1,0,1,0]
=> [1,2] => [1,2] => [1,0,1,0]
=> 2
[1,1,0,0]
=> [2,1] => [2,1] => [1,1,0,0]
=> ? = 1
[1,0,1,0,1,0]
=> [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,0]
=> [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,0]
=> [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,0]
=> [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
=> ? ∊ {1,1}
[1,1,1,0,0,0]
=> [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? ∊ {1,1}
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,1,0,1,1,0,0,0]
=> [2,4,3,1] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,1,1,0,0,0,1,0]
=> [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [3,2,4,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,1,1,0,1,0,0,0]
=> [4,2,3,1] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 2
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1}
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,0,0,1,0,1,0]
=> [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [3,2,4,1,5] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,1,0,0,0,1,0]
=> [4,2,3,1,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,0,1,0,1,0,0,0]
=> [5,2,3,4,1] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,1,1,0,0,0,0,1,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,1,1,1,0,0,1,0,0,0]
=> [5,3,2,4,1] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [5,3,4,2,1] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,1,1,1,0,0,0,0,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,5,1] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,5,4,6,1] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,5,4,1] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,3,5,6,1] => [6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,3,6,5,1] => [6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,5,3,4,6,1] => [6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,5,4,3,6,1] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,5,4,3,1] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,2,4,5,6,1] => [6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,2,4,6,5,1] => [6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,5,4,6,1] => [6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,2,6,5,4,1] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,2,3,5,6,1] => [6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,2,3,6,5,1] => [6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,2,3,4,6,1] => [6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,4,3,6,1] => [6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,3,2,5,6,1] => [6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,3,2,6,5,1] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,2,4,6,1] => [6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,3,4,2,6,1] => [6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,4,3,2,6,1] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3}
Description
The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.
Matching statistic: St000260
(load all 34 compositions to match this statistic)
(load all 34 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 70% ●values known / values provided: 70%●distinct values known / distinct values provided: 100%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 70% ●values known / values provided: 70%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => ([],1)
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0]
=> [2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,0]
=> [1,2] => ([],2)
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0,1,0]
=> [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,0,1,1,0,0]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,0,1,0]
=> [3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,1,0,0]
=> [2,1,3] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? = 1 - 1
[1,1,1,0,0,0]
=> [1,2,3] => ([],3)
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => ([(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)
=> 1 = 2 - 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,2} - 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2} - 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2} - 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,2} - 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([],4)
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => ([(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)
=> 1 = 2 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => ([(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),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => ([(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),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => ([(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),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => ([(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)
=> 1 = 2 - 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 1 = 2 - 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 1 = 2 - 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2} - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([],5)
=> ([],1)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 2 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 2 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 2 - 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [4,5,3,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,4,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,5,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [5,4,2,3,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [4,5,2,3,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,4,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [4,3,2,5,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,4,2,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [5,2,3,4,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [4,2,3,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [4,5,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [4,3,5,1,2,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [5,4,2,1,3,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,5,2,1,3,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,3,2,1,4,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,4,2,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,3,1,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,2,3,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,2,4,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2)],3)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2} - 1
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000514
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000514: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 69%●distinct values known / distinct values provided: 33%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000514: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 69%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [1] => [1]
=> []
=> ? = 1
[1,0,1,0]
=> [2,1] => [1,1]
=> [1]
=> ? ∊ {1,2}
[1,1,0,0]
=> [1,2] => [2]
=> []
=> ? ∊ {1,2}
[1,0,1,0,1,0]
=> [2,3,1] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,0,1,1,0,0]
=> [2,1,3] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,1,0,0,1,0]
=> [1,3,2] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,1,0,1,0,0]
=> [3,1,2] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,1,1,0,0,0]
=> [1,2,3] => [3]
=> []
=> ? ∊ {1,1,2,2,2}
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> 2
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => [2,2]
=> [2]
=> 2
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => [2,2]
=> [2]
=> 2
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,0,1,0,0,0]
=> [4,1,2,3] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4]
=> []
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => [3,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,3,1,4,6,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,6,4,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,3,6,1,4,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [2,1,4,5,6,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [2,1,4,5,3,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,6,3,5] => [3,3]
=> [3]
=> 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [2,1,4,3,5,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,4,1,5,6,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [2,4,1,5,3,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,4,5,1,6,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [2,4,5,6,1,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [2,4,5,1,3,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,6,5] => [3,3]
=> [3]
=> 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,3,4,5,6,2] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,3,4,5,2,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,3,4,2,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,1,2,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,2,4,5,6,3] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,2,4,5,3,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,2,4,3,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,2,3,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [4,1,2,3,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
Description
The number of invariant simple graphs when acting with a permutation of given cycle type.
Matching statistic: St000515
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000515: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 69%●distinct values known / distinct values provided: 33%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000515: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 69%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [1] => [1]
=> []
=> ? = 1
[1,0,1,0]
=> [2,1] => [1,1]
=> [1]
=> ? ∊ {1,2}
[1,1,0,0]
=> [1,2] => [2]
=> []
=> ? ∊ {1,2}
[1,0,1,0,1,0]
=> [2,3,1] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,0,1,1,0,0]
=> [2,1,3] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,1,0,0,1,0]
=> [1,3,2] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,1,0,1,0,0]
=> [3,1,2] => [2,1]
=> [1]
=> ? ∊ {1,1,2,2,2}
[1,1,1,0,0,0]
=> [1,2,3] => [3]
=> []
=> ? ∊ {1,1,2,2,2}
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> 2
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => [2,2]
=> [2]
=> 2
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => [2,2]
=> [2]
=> 2
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,0,1,0,0,0]
=> [4,1,2,3] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4]
=> []
=> ? ∊ {1,1,1,1,2,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => [3,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => [3,2]
=> [2]
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,3,1,4,6,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,6,4,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,3,6,1,4,5] => [4,2]
=> [2]
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [2,1,4,5,6,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [2,1,4,5,3,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,6,3,5] => [3,3]
=> [3]
=> 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [2,1,4,3,5,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,4,1,5,6,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [2,4,1,5,3,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,4,5,1,6,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [2,4,5,6,1,3] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [2,4,5,1,3,6] => [4,2]
=> [2]
=> 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,6,5] => [3,3]
=> [3]
=> 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,3,4,5,6,2] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,3,4,5,2,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,3,4,2,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,1,2,4,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,2,4,5,6,3] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,2,4,5,3,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,2,4,3,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,2,3,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [4,1,2,3,5,6] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3}
Description
The number of invariant set partitions when acting with a permutation of given cycle type.
Matching statistic: St000630
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000630: Binary words ⟶ ℤResult quality: 33% ●values known / values provided: 68%●distinct values known / distinct values provided: 33%
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000630: Binary words ⟶ ℤResult quality: 33% ●values known / values provided: 68%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [[1],[]]
=> []
=> => ? = 1
[1,0,1,0]
=> [[1,1],[]]
=> []
=> => ? ∊ {1,2}
[1,1,0,0]
=> [[2],[]]
=> []
=> => ? ∊ {1,2}
[1,0,1,0,1,0]
=> [[1,1,1],[]]
=> []
=> => ? ∊ {1,1,2,2}
[1,0,1,1,0,0]
=> [[2,1],[]]
=> []
=> => ? ∊ {1,1,2,2}
[1,1,0,0,1,0]
=> [[2,2],[1]]
=> [1]
=> 10 => 2
[1,1,0,1,0,0]
=> [[3],[]]
=> []
=> => ? ∊ {1,1,2,2}
[1,1,1,0,0,0]
=> [[2,2],[]]
=> []
=> => ? ∊ {1,1,2,2}
[1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [1,1]
=> 110 => 2
[1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> [1]
=> 10 => 2
[1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> 100 => 2
[1,1,0,1,0,1,0,0]
=> [[4],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,1,0,1,1,0,0,0]
=> [[3,3],[1]]
=> [1]
=> 10 => 2
[1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> [1]
=> 10 => 2
[1,1,1,0,0,1,0,0]
=> [[3,2],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> []
=> => ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [1,1]
=> 110 => 2
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> 100 => 2
[1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> 1110 => 2
[1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [1,1]
=> 110 => 2
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [2,1]
=> 1010 => 2
[1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> [1]
=> 10 => 2
[1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> 110 => 2
[1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> 1100 => 2
[1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> 100 => 2
[1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> 1000 => 2
[1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 100 => 2
[1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 1010 => 2
[1,1,0,1,1,0,0,1,0,0]
=> [[4,3],[1]]
=> [1]
=> 10 => 2
[1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 110 => 2
[1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> [1]
=> 10 => 2
[1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> 110 => 2
[1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> [1]
=> 10 => 2
[1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 100 => 2
[1,1,1,0,0,1,0,1,0,0]
=> [[4,2],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2],[1]]
=> [1]
=> 10 => 2
[1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> [1]
=> 10 => 2
[1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 100 => 2
[1,1,1,1,0,0,0,1,0,0]
=> [[4,3],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3],[1]]
=> [1]
=> 10 => 2
[1,1,1,1,0,1,0,0,0,0]
=> [[4,4],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> [1,1]
=> 110 => 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1,1],[2]]
=> [2]
=> 100 => 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[4,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1,1]]
=> [1,1,1]
=> 1110 => 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> [1,1]
=> 110 => 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> [2,1]
=> 1010 => 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> [1,1]
=> 110 => 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1],[2,2]]
=> [2,2]
=> 1100 => 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> [2]
=> 100 => 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[4,4,1],[3]]
=> [3]
=> 1000 => 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[5,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[4,4,1],[2]]
=> [2]
=> 100 => 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> [2,1]
=> 1010 => 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> [1]
=> 10 => 2
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [[4,2,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [[4,3,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [[4,4,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [[6],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [[5,2],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [[4,2,2],[]]
=> []
=> => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
Description
The length of the shortest palindromic decomposition of a binary word.
A palindromic decomposition (paldec for short) of a word $w=a_1,\dots,a_n$ is any list of factors $p_1,\dots,p_k$ such that $w=p_1\dots p_k$ and each $p_i$ is a palindrome, i.e. coincides with itself read backwards.
Matching statistic: St001165
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001165: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 68%●distinct values known / distinct values provided: 33%
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001165: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 68%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [[1],[]]
=> []
=> []
=> ? = 1
[1,0,1,0]
=> [[1,1],[]]
=> []
=> []
=> ? ∊ {1,2}
[1,1,0,0]
=> [[2],[]]
=> []
=> []
=> ? ∊ {1,2}
[1,0,1,0,1,0]
=> [[1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,0,1,1,0,0]
=> [[2,1],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,1,0,0,1,0]
=> [[2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,0,0]
=> [[3],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,1,1,0,0,0]
=> [[2,2],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [[4],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,0,1,1,0,0,0]
=> [[3,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [[3,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [[4,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [[4,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [[4,3],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [[4,4],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[4,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[4,4,1],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[5,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[4,4,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [[4,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [[4,3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [[4,4,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [[6],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [[5,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [[4,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
Description
Number of simple modules with even projective dimension in the corresponding Nakayama algebra.
Matching statistic: St001471
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001471: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 68%●distinct values known / distinct values provided: 33%
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001471: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 68%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [[1],[]]
=> []
=> []
=> ? = 1
[1,0,1,0]
=> [[1,1],[]]
=> []
=> []
=> ? ∊ {1,2}
[1,1,0,0]
=> [[2],[]]
=> []
=> []
=> ? ∊ {1,2}
[1,0,1,0,1,0]
=> [[1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,0,1,1,0,0]
=> [[2,1],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,1,0,0,1,0]
=> [[2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,0,0]
=> [[3],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,1,1,0,0,0]
=> [[2,2],[]]
=> []
=> []
=> ? ∊ {1,1,2,2}
[1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [[4],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,0,1,1,0,0,0]
=> [[3,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [[3,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [[4,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [[4,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [[4,3],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [[4,4],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[4,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[4,4,1],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[5,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[4,4,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [[4,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [[4,3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [[4,4,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [[6],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [[5,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [[4,2,2],[]]
=> []
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3}
Description
The magnitude of a Dyck path.
The magnitude of a finite dimensional algebra with invertible Cartan matrix C is defined as the sum of all entries of the inverse of C.
We define the magnitude of a Dyck path as the magnitude of the corresponding LNakayama algebra.
Matching statistic: St000259
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 67%●distinct values known / distinct values provided: 33%
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 67%●distinct values known / distinct values provided: 33%
Values
[1,0]
=> [1,1,0,0]
=> [2] => ([],2)
=> ? = 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [2,1] => ([(0,2),(1,2)],3)
=> 2
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [3] => ([],3)
=> ? = 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {1,1}
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [4] => ([],4)
=> ? ∊ {1,1}
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,2}
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,2}
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,2}
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,2}
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [5] => ([],5)
=> ? ∊ {1,1,1,1,2}
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [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)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [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)
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [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)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [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)
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [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)
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,4] => ([(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [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)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [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)
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [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)
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [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)
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [6] => ([],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(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)
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [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)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [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)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [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)
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [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
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [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
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [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
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [2,5] => ([(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [3,1,1,2] => ([(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)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [3,1,1,2] => ([(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)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,1,0,0,1,1,0,0,0]
=> [3,1,1,2] => ([(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)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [3,1,1,2] => ([(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)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3}
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
The following 80 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000542The number of left-to-right-minima of a permutation. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St000455The second largest eigenvalue of a graph if it is integral. St000741The Colin de Verdière graph invariant. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St000058The order of a permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001060The distinguishing index of a graph. St001096The size of the overlap set of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000996The number of exclusive left-to-right maxima of a permutation. St000451The length of the longest pattern of the form k 1 2. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000314The number of left-to-right-maxima of a permutation. St000654The first descent of a permutation. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001273The projective dimension of the first term in an injective coresolution of the regular module. St000485The length of the longest cycle of a permutation. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001948The number of augmented double ascents of a permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001545The second Elser number of a connected graph. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001568The smallest positive integer that does not appear twice in the partition. St000145The Dyson rank of a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000478Another weight of a partition according to Alladi. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. St000939The number of characters of the symmetric group whose value on the partition is positive. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001569The maximal modular displacement of a permutation. St000298The order dimension or Dushnik-Miller dimension of a poset. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000307The number of rowmotion orbits of a poset. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St001728The number of invisible descents of a permutation. St001330The hat guessing number of a graph. St000768The number of peaks in an integer composition. St000891The number of distinct diagonal sums of a permutation matrix. St000640The rank of the largest boolean interval in a poset. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000668The least common multiple of the parts of the partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St000993The multiplicity of the largest part of an integer partition. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St000764The number of strong records in an integer composition. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St001737The number of descents of type 2 in a permutation. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001730The number of times the path corresponding to a binary word crosses the base line. St001960The number of descents of a permutation minus one if its first entry is not one. St000633The size of the automorphism group of a poset. St001399The distinguishing number of a poset. St000850The number of 1/2-balanced pairs in a poset. St001621The number of atoms of a lattice. St001624The breadth of a lattice. St000454The largest eigenvalue of a graph if it is integral.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!