Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001090
(load all 5 compositions to match this statistic)
Mapping
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001090: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => 0
[1,0,1,0]
 => [2,1] => 1
[1,1,0,0]
 => [1,2] => 0
[1,0,1,0,1,0]
 => [3,2,1] => 1
[1,0,1,1,0,0]
 => [2,3,1] => 2
[1,1,0,0,1,0]
 => [3,1,2] => 2
[1,1,0,1,0,0]
 => [2,1,3] => 1
[1,1,1,0,0,0]
 => [1,2,3] => 0
[1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 1
[1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 3
[1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 3
[1,0,1,1,0,1,0,0]
 => [3,2,4,1] => 3
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 3
[1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 3
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 3
[1,1,0,1,0,0,1,0]
 => [4,2,1,3] => 2
[1,1,0,1,0,1,0,0]
 => [3,2,1,4] => 1
[1,1,0,1,1,0,0,0]
 => [2,3,1,4] => 2
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 3
[1,1,1,0,0,1,0,0]
 => [3,1,2,4] => 2
[1,1,1,0,1,0,0,0]
 => [2,1,3,4] => 1
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => 1
[1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => 4
[1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => 4
[1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => 4
[1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => 4
[1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => 4
[1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => 4
[1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => 4
[1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => 4
[1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => 4
[1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => 3
[1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => 3
[1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => 4
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 4
[1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => 4
[1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => 3
[1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => 4
[1,1,0,0,1,1,0,1,0,0]
 => [4,3,5,1,2] => 4
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => 4
[1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => 3
[1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => 4
[1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => 2
[1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => 1
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => 3
[1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => 4
[1,1,0,1,1,0,0,1,0,0]
 => [4,2,3,1,5] => 3
[1,1,0,1,1,0,1,0,0,0]
 => [3,2,4,1,5] => 3
[1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => 3
Description
The number of pop-stack-sorts needed to sort a permutation. The pop-stack sorting operator is defined as follows. Process the permutation $\pi$ from left to right. If the stack is empty or its top element is smaller than the current element, empty the stack completely and append its elements to the output in reverse order. Next, push the current element onto the stack. After having processed the last entry, append the stack to the output in reverse order. A permutation is $t$-pop-stack sortable if it is sortable using $t$ pop-stacks in series.
Matching statistic: St001232
(load all 3 compositions to match this statistic)
Mapping
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 64%
Values
[1,0]
 => [1] => [1,0]
 => [1,0]
 => 0
[1,0,1,0]
 => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 1
[1,1,0,0]
 => [1,2] => [1,0,1,0]
 => [1,1,0,0]
 => 0
[1,0,1,0,1,0]
 => [3,2,1] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 1
[1,0,1,1,0,0]
 => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[1,1,0,0,1,0]
 => [3,1,2] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2
[1,1,0,1,0,0]
 => [2,1,3] => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[1,1,1,0,0,0]
 => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
[1,0,1,0,1,0,1,0]
 => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,1,0,0]
 => [3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => ? = 3
[1,0,1,1,0,0,1,0]
 => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 3
[1,0,1,1,0,1,0,0]
 => [3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[1,1,0,0,1,0,1,0]
 => [4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 3
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => ? = 3
[1,1,0,1,0,0,1,0]
 => [4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2
[1,1,0,1,0,1,0,0]
 => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1
[1,1,0,1,1,0,0,0]
 => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 3
[1,1,1,0,0,1,0,0]
 => [3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,0,1,0,0,0]
 => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ? = 4
[1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => ? = 4
[1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ? = 4
[1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
[1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ? = 3
[1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,0,1,0,0]
 => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => ? = 4
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ? = 4
[1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3
[1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ? = 4
[1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2
[1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => ? = 3
[1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,1,1,0,0,1,0,0]
 => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 3
[1,1,0,1,1,0,1,0,0,0]
 => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ? = 4
[1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3
[1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 3
[1,1,1,0,0,1,1,0,0,0]
 => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => ? = 3
[1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3
[1,1,1,0,1,0,0,1,0,0]
 => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2
[1,1,1,0,1,0,1,0,0,0]
 => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1
[1,1,1,0,1,1,0,0,0,0]
 => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 3
[1,1,1,1,0,0,1,0,0,0]
 => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,1,0,0,0,0]
 => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 5
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 5
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => 5
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => 5
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 5
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 4
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 3
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000075
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000075: Standard tableaux ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 18%
Values
[1,0]
 => []
 => []
 => ?
 => ? = 0 + 1
[1,0,1,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,0,0]
 => []
 => []
 => ?
 => ? = 0 + 1
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 3 = 2 + 1
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 3 = 2 + 1
[1,1,0,1,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,0,0,0]
 => []
 => []
 => ?
 => ? = 0 + 1
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => ? = 1 + 1
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => ? = 3 + 1
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => ? = 3 + 1
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => ? = 3 + 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => ? = 3 + 1
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => ? = 3 + 1
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => ? = 3 + 1
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => ? = 2 + 1
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 3 = 2 + 1
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => ? = 3 + 1
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 3 = 2 + 1
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,0,0,0,0]
 => []
 => []
 => ?
 => ? = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [[1,3,5,7,9],[2,4,6,8,10]]
 => ? = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [[1,3,5,7,8],[2,4,6,9,10]]
 => ? = 4 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[1,3,5,6,9],[2,4,7,8,10]]
 => ? = 4 + 1
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [[1,3,5,6,8],[2,4,7,9,10]]
 => ? = 4 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[1,3,5,6,7],[2,4,8,9,10]]
 => ? = 4 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[1,3,4,7,9],[2,5,6,8,10]]
 => ? = 4 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[1,3,4,7,8],[2,5,6,9,10]]
 => ? = 4 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [[1,3,4,6,9],[2,5,7,8,10]]
 => ? = 4 + 1
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [[1,3,4,6,8],[2,5,7,9,10]]
 => ? = 4 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[1,3,4,6,7],[2,5,8,9,10]]
 => ? = 4 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[1,3,4,5,9],[2,6,7,8,10]]
 => ? = 3 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 3 + 1
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [[1,3,4,5,7],[2,6,8,9,10]]
 => ? = 4 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[1,3,4,5,6],[2,7,8,9,10]]
 => ? = 4 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[1,2,5,7,9],[3,4,6,8,10]]
 => ? = 4 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[1,2,5,7,8],[3,4,6,9,10]]
 => ? = 3 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[1,2,5,6,9],[3,4,7,8,10]]
 => ? = 4 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[1,2,5,6,8],[3,4,7,9,10]]
 => ? = 4 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[1,2,5,6,7],[3,4,8,9,10]]
 => ? = 4 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[1,2,4,7,9],[3,5,6,8,10]]
 => ? = 3 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[1,2,4,7,8],[3,5,6,9,10]]
 => ? = 4 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[1,2,4,6,9],[3,5,7,8,10]]
 => ? = 2 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => ? = 3 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[1,2,4,5,9],[3,6,7,8,10]]
 => ? = 4 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => ? = 3 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => ? = 3 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => ? = 3 + 1
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[1,2,3,7,9],[4,5,6,8,10]]
 => ? = 4 + 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[1,2,3,7,8],[4,5,6,9,10]]
 => ? = 4 + 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[1,2,3,6,9],[4,5,7,8,10]]
 => ? = 3 + 1
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => ? = 3 + 1
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => ? = 3 + 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[1,2,3,5,9],[4,6,7,8,10]]
 => ? = 3 + 1
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => ? = 2 + 1
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 3 = 2 + 1
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[1,2,3,4,9],[5,6,7,8,10]]
 => ? = 4 + 1
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => ? = 3 + 1
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 3 = 2 + 1
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 3 = 2 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 3 = 2 + 1
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 3 = 2 + 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 3 = 2 + 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 2 = 1 + 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 2 = 1 + 1
Description
The orbit size of a standard tableau under promotion.
Matching statistic: St001645
Mapping
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 64%
Values
[1,0]
 => [1] => [1] => ([],1)
 => 1 = 0 + 1
[1,0,1,0]
 => [2,1] => [2,1] => ([(0,1)],2)
 => 2 = 1 + 1
[1,1,0,0]
 => [1,2] => [1,2] => ([],2)
 => ? = 0 + 1
[1,0,1,0,1,0]
 => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 1 + 1
[1,0,1,1,0,0]
 => [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
[1,1,0,0,1,0]
 => [3,1,2] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
[1,1,0,1,0,0]
 => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 1 + 1
[1,1,1,0,0,0]
 => [1,2,3] => [1,2,3] => ([],3)
 => ? = 0 + 1
[1,0,1,0,1,0,1,0]
 => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1 + 1
[1,0,1,0,1,1,0,0]
 => [2,4,1,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4 = 3 + 1
[1,0,1,1,0,0,1,0]
 => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 3 + 1
[1,0,1,1,0,1,0,0]
 => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[1,1,0,0,1,0,1,0]
 => [3,1,4,2] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[1,1,0,1,0,0,1,0]
 => [3,1,2,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[1,1,0,1,0,1,0,0]
 => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 1 + 1
[1,1,0,1,1,0,0,0]
 => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
[1,1,1,0,0,1,0,0]
 => [1,4,2,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[1,1,1,0,1,0,0,0]
 => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 1 + 1
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
 => [2,1,4,3,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
 => ? = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 4 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [2,1,4,5,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,0,1,1,0,1,0,0]
 => [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,4,5,1,3] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [2,1,5,3,4] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [2,5,1,3,4] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [2,1,3,5,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
 => ? = 4 + 1
[1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [2,3,5,1,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,4,5] => [2,1,3,4,5] => ([(3,4)],5)
 => ? = 3 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [2,3,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,0,1,1,1,0,1,0,0,0]
 => [2,3,4,1,5] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [3,1,4,2,5] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [3,4,1,2,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [3,1,4,5,2] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,4,1,5,2] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [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)
 => 5 = 4 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,5,1,2,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 5 = 4 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [3,1,2,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,3,5,2,4] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ? = 3 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,3,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 3 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,3,4,2,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,3,4,5,2] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,1,0,0,0,1,0,1,0]
 => [4,1,5,2,3] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => [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)
 => 5 = 4 + 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,1,2,5,3] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,1,0,0,1,0,1,0,0]
 => [1,4,2,5,3] => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,1,0,0,1,1,0,0,0]
 => [1,4,5,2,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,1,2,3,5] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,1,0,1,0,0,1,0,0]
 => [1,4,2,3,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,1,1,0,1,0,1,0,0,0]
 => [1,2,4,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 1 + 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,2,4,5,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [2,4,6,1,3,5] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => 6 = 5 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,4,5,6,1,3] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 6 = 5 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [2,5,6,1,3,4] => [4,6,5,1,3,2] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [3,4,6,1,2,5] => [5,4,6,2,1,3] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [3,4,5,6,1,2] => [6,5,3,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [3,5,1,6,2,4] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 6 = 5 + 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [3,5,6,1,2,4] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6 = 5 + 1
[1,1,1,0,0,0,1,1,0,1,0,0]
 => [4,5,1,6,2,3] => [6,5,3,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [4,5,6,1,2,3] => [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)
 => 6 = 5 + 1
[1,1,1,0,1,0,0,0,1,1,0,0]
 => [4,6,1,2,3,5] => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 6 = 5 + 1
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [5,6,1,2,3,4] => [6,5,3,4,2,1] => ([(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)
 => 6 = 5 + 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [3,4,5,6,7,1,2] => [7,6,3,4,5,2,1] => ([(0,3),(0,4),(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)
 => 7 = 6 + 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => [4,5,1,6,7,2,3] => [7,6,3,4,5,2,1] => ([(0,3),(0,4),(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)
 => 7 = 6 + 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
 => [4,5,6,1,7,2,3] => [7,6,4,3,5,2,1] => ([(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)
 => 7 = 6 + 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [5,6,7,1,2,3,4] => [7,6,5,4,3,2,1] => ([(0,1),(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)
 => 7 = 6 + 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [6,7,1,2,3,4,5] => [7,6,3,4,5,2,1] => ([(0,3),(0,4),(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)
 => 7 = 6 + 1
Description
The pebbling number of a connected graph.