Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000706
Mapping
St000706: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 1
[1,1]
 => 2
[3]
 => 1
[2,1]
 => 1
[1,1,1]
 => 6
[4]
 => 1
[3,1]
 => 1
[2,2]
 => 2
[2,1,1]
 => 2
[1,1,1,1]
 => 24
[5]
 => 1
[4,1]
 => 1
[3,2]
 => 1
[3,1,1]
 => 2
[2,2,1]
 => 2
[2,1,1,1]
 => 6
[1,1,1,1,1]
 => 120
[6]
 => 1
[5,1]
 => 1
[4,2]
 => 1
[4,1,1]
 => 2
[3,3]
 => 2
[3,2,1]
 => 1
[3,1,1,1]
 => 6
[2,2,2]
 => 6
[2,2,1,1]
 => 4
[2,1,1,1,1]
 => 24
[1,1,1,1,1,1]
 => 720
[7]
 => 1
[6,1]
 => 1
[5,2]
 => 1
[5,1,1]
 => 2
[4,3]
 => 1
[4,2,1]
 => 1
[4,1,1,1]
 => 6
[3,3,1]
 => 2
[3,2,2]
 => 2
[3,2,1,1]
 => 2
[3,1,1,1,1]
 => 24
[2,2,2,1]
 => 6
[2,2,1,1,1]
 => 12
[2,1,1,1,1,1]
 => 120
[1,1,1,1,1,1,1]
 => 5040
[8]
 => 1
[7,1]
 => 1
[6,2]
 => 1
[6,1,1]
 => 2
[5,3]
 => 1
[5,2,1]
 => 1
[5,1,1,1]
 => 6
Description
The product of the factorials of the multiplicities of an integer partition.
Matching statistic: St000417
Mapping
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
St000417: Ordered trees ⟶ ℤResult quality: 43% ●values known / values provided: 43%●distinct values known / distinct values provided: 54%
Values
[2]
 => [1,0,1,0]
 => [1,1,0,0]
 => [[[]]]
 => 1
[1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => [[],[]]
 => 2
[3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => [[[[]]]]
 => 1
[2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => [[[]],[]]
 => 1
[1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [[],[],[]]
 => 6
[4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => 1
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [[[[]]],[]]
 => 1
[2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => [[[],[]]]
 => 2
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => [[[]],[],[]]
 => 2
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [[],[],[],[]]
 => 24
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => 1
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[[[[]]]],[]]
 => 1
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => [[[[]],[]]]
 => 1
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[[[]]],[],[]]
 => 2
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => [[[],[]],[]]
 => 2
[2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[[]],[],[],[]]
 => 6
[1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[]]
 => 120
[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]
 => [[[[[[[]]]]]]]
 => 1
[5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [[[[[[]]]]],[]]
 => 1
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[[[[]]],[]]]
 => 1
[4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [[[[[]]]],[],[]]
 => 2
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [[[[],[]]]]
 => 2
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[[[]],[]],[]]
 => 1
[3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [[[[]]],[],[],[]]
 => 6
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => [[[],[],[]]]
 => 6
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[[],[]],[],[]]
 => 4
[2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [[[]],[],[],[],[]]
 => 24
[1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[],[]]
 => 720
[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]
 => [[[[[[[[]]]]]]]]
 => 1
[6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [[[[[[[]]]]]],[]]
 => 1
[5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [[[[[[]]]],[]]]
 => 1
[5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [[[[[[]]]]],[],[]]
 => 2
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [[[[[]],[]]]]
 => 1
[4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [[[[[]]],[]],[]]
 => 1
[4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [[[[[]]]],[],[],[]]
 => 6
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[[[],[]]],[]]
 => 2
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[[[]],[],[]]]
 => 2
[3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [[[[]],[]],[],[]]
 => 2
[3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [[[[]]],[],[],[],[]]
 => 24
[2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[[],[],[]],[]]
 => 6
[2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [[[],[]],[],[],[]]
 => 12
[2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[[]],[],[],[],[],[]]
 => 120
[1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[],[],[]]
 => 5040
[8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [[[[[[[[[]]]]]]]]]
 => ? = 1
[7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [[[[[[[[]]]]]]],[]]
 => ? = 1
[6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [[[[[[[]]]]],[]]]
 => 1
[6,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
 => [[[[[[[]]]]]],[],[]]
 => ? = 2
[5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [[[[[[]]],[]]]]
 => 1
[5,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
 => [[[[[[]]]],[]],[]]
 => 1
[5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
 => [[[[[[]]]]],[],[],[]]
 => ? = 6
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [[[[[],[]]]]]
 => 2
[4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [[[[[]],[]]],[]]
 => 1
[4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [[[[[]]],[],[]]]
 => 2
[4,2,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [[[[[]]],[]],[],[]]
 => 2
[4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
 => [[[[[]]]],[],[],[],[]]
 => ? = 24
[9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => [[[[[[[[[[]]]]]]]]]]
 => ? = 1
[8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [[[[[[[[[]]]]]]]],[]]
 => ? = 1
[7,2]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
 => [[[[[[[[]]]]]],[]]]
 => ? = 1
[7,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
 => [[[[[[[[]]]]]]],[],[]]
 => ? = 2
[6,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
 => [[[[[[[]]]]],[]],[]]
 => ? = 1
[6,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
 => [[[[[[[]]]]]],[],[],[]]
 => ? = 6
[5,2,1,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
 => [[[[[[]]]],[]],[],[]]
 => ? = 2
[5,1,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
 => [[[[[[]]]]],[],[],[],[]]
 => ? = 24
[4,2,1,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
 => [[[[[]]],[]],[],[],[]]
 => ? = 6
[4,1,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[[[[]]]],[],[],[],[],[]]
 => ? = 120
[3,2,1,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
 => [[[[]],[]],[],[],[],[]]
 => ? = 24
[3,1,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[[[]]],[],[],[],[],[],[]]
 => ? = 720
[2,1,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[[]],[],[],[],[],[],[],[]]
 => ? = 5040
[1,1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[],[],[],[],[]]
 => ? = 362880
[10]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
 => [[[[[[[[[[[]]]]]]]]]]]
 => ? = 1
[9,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
 => [[[[[[[[[[]]]]]]]]],[]]
 => ? = 1
[8,2]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
 => [[[[[[[[[]]]]]]],[]]]
 => ? = 1
[8,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
 => [[[[[[[[[]]]]]]]],[],[]]
 => ? = 2
[7,3]
 => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
 => [[[[[[[[]]]]],[]]]]
 => ? = 1
[7,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
 => [[[[[[[[]]]]]],[]],[]]
 => ? = 1
[7,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
 => [[[[[[[[]]]]]]],[],[],[]]
 => ? = 6
[6,3,1]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
 => [[[[[[[]]]],[]]],[]]
 => ? = 1
[6,2,2]
 => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
 => [[[[[[[]]]]],[],[]]]
 => ? = 2
[6,2,1,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
 => [[[[[[[]]]]],[]],[],[]]
 => ? = 2
[6,1,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
 => [[[[[[[]]]]]],[],[],[],[]]
 => ? = 24
[5,3,1,1]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
 => [[[[[[]]],[]]],[],[]]
 => ? = 2
[5,2,2,1]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
 => [[[[[[]]]],[],[]],[]]
 => ? = 2
[5,2,1,1,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
 => [[[[[[]]]],[]],[],[],[]]
 => ? = 6
[5,1,1,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[[[[[]]]]],[],[],[],[],[]]
 => ? = 120
[4,3,1,1,1]
 => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
 => [[[[[]],[]]],[],[],[]]
 => ? = 6
[4,2,2,1,1]
 => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
 => [[[[[]]],[],[]],[],[]]
 => ? = 4
[4,2,1,1,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
 => [[[[[]]],[]],[],[],[],[]]
 => ? = 24
[4,1,1,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[[[[]]]],[],[],[],[],[],[]]
 => ? = 720
[3,3,1,1,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
 => [[[[],[]]],[],[],[],[]]
 => ? = 48
[3,2,2,1,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
 => [[[[]],[],[]],[],[],[]]
 => ? = 12
[3,2,1,1,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[[[]],[]],[],[],[],[],[]]
 => ? = 120
[3,1,1,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[[[]]],[],[],[],[],[],[],[]]
 => ? = 5040
[2,2,2,1,1,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [[[],[],[]],[],[],[],[]]
 => ? = 144
[2,2,1,1,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[[],[]],[],[],[],[],[],[]]
 => ? = 1440
[2,1,1,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[[]],[],[],[],[],[],[],[],[]]
 => ? = 40320
[1,1,1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[],[],[],[],[],[]]
 => ? = 3628800
[11]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
 => [[[[[[[[[[[[]]]]]]]]]]]]
 => ? = 1
[10,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
 => [[[[[[[[[[[]]]]]]]]]],[]]
 => ? = 1
[9,2]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
 => [[[[[[[[[[]]]]]]]],[]]]
 => ? = 1
[9,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
 => [[[[[[[[[[]]]]]]]]],[],[]]
 => ? = 2
Description
The size of the automorphism group of the ordered tree.
Matching statistic: St000633
Mapping
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000633: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 38%
Values
[2]
 => [[1,2]]
 => [1,2] => ([(0,1)],2)
 => 1
[1,1]
 => [[1],[2]]
 => [2,1] => ([],2)
 => 2
[3]
 => [[1,2,3]]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 1
[2,1]
 => [[1,2],[3]]
 => [3,1,2] => ([(1,2)],3)
 => 1
[1,1,1]
 => [[1],[2],[3]]
 => [3,2,1] => ([],3)
 => 6
[4]
 => [[1,2,3,4]]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 1
[3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => 1
[2,2]
 => [[1,2],[3,4]]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => 2
[2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => ([(2,3)],4)
 => 2
[1,1,1,1]
 => [[1],[2],[3],[4]]
 => [4,3,2,1] => ([],4)
 => 24
[5]
 => [[1,2,3,4,5]]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,1]
 => [[1,2,3,4],[5]]
 => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
 => 1
[3,2]
 => [[1,2,3],[4,5]]
 => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => 1
[3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => ([(2,3),(3,4)],5)
 => 2
[2,2,1]
 => [[1,2],[3,4],[5]]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => 2
[2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => ([(3,4)],5)
 => 6
[1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => ([],5)
 => 120
[6]
 => [[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,1]
 => [[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
 => 1
[4,2]
 => [[1,2,3,4],[5,6]]
 => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
 => 1
[4,1,1]
 => [[1,2,3,4],[5],[6]]
 => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
 => 2
[3,3]
 => [[1,2,3],[4,5,6]]
 => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
 => 2
[3,2,1]
 => [[1,2,3],[4,5],[6]]
 => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6)
 => 1
[3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
 => 6
[2,2,2]
 => [[1,2],[3,4],[5,6]]
 => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
 => 6
[2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
 => 4
[2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [6,5,4,3,1,2] => ([(4,5)],6)
 => 24
[1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => ([],6)
 => 720
[7]
 => [[1,2,3,4,5,6,7]]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ? = 1
[6,1]
 => [[1,2,3,4,5,6],[7]]
 => [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
 => ? = 1
[5,2]
 => [[1,2,3,4,5],[6,7]]
 => [6,7,1,2,3,4,5] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
 => ? = 1
[5,1,1]
 => [[1,2,3,4,5],[6],[7]]
 => [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7)
 => ? = 2
[4,3]
 => [[1,2,3,4],[5,6,7]]
 => [5,6,7,1,2,3,4] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
 => ? = 1
[4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ([(1,6),(2,4),(5,3),(6,5)],7)
 => ? = 1
[4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7)
 => 6
[3,3,1]
 => [[1,2,3],[4,5,6],[7]]
 => [7,4,5,6,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7)
 => ? = 2
[3,2,2]
 => [[1,2,3],[4,5],[6,7]]
 => [6,7,4,5,1,2,3] => ([(0,5),(1,4),(2,6),(6,3)],7)
 => ? = 2
[3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ([(2,4),(3,5),(5,6)],7)
 => ? = 2
[3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7)
 => 24
[2,2,2,1]
 => [[1,2],[3,4],[5,6],[7]]
 => [7,5,6,3,4,1,2] => ([(1,6),(2,5),(3,4)],7)
 => ? = 6
[2,2,1,1,1]
 => [[1,2],[3,4],[5],[6],[7]]
 => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7)
 => 12
[2,1,1,1,1,1]
 => [[1,2],[3],[4],[5],[6],[7]]
 => [7,6,5,4,3,1,2] => ([(5,6)],7)
 => 120
[1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => [7,6,5,4,3,2,1] => ([],7)
 => 5040
[8]
 => [[1,2,3,4,5,6,7,8]]
 => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 1
[7,1]
 => [[1,2,3,4,5,6,7],[8]]
 => [8,1,2,3,4,5,6,7] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
 => ? = 1
[6,2]
 => [[1,2,3,4,5,6],[7,8]]
 => [7,8,1,2,3,4,5,6] => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8)
 => ? = 1
[6,1,1]
 => [[1,2,3,4,5,6],[7],[8]]
 => [8,7,1,2,3,4,5,6] => ([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
 => ? = 2
[5,3]
 => [[1,2,3,4,5],[6,7,8]]
 => [6,7,8,1,2,3,4,5] => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)
 => ? = 1
[5,2,1]
 => [[1,2,3,4,5],[6,7],[8]]
 => [8,6,7,1,2,3,4,5] => ([(1,7),(2,4),(5,6),(6,3),(7,5)],8)
 => ? = 1
[5,1,1,1]
 => [[1,2,3,4,5],[6],[7],[8]]
 => [8,7,6,1,2,3,4,5] => ([(3,4),(4,7),(6,5),(7,6)],8)
 => ? = 6
[4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
 => ? = 2
[4,3,1]
 => [[1,2,3,4],[5,6,7],[8]]
 => [8,5,6,7,1,2,3,4] => ([(1,6),(2,7),(5,4),(6,5),(7,3)],8)
 => ? = 1
[4,2,2]
 => [[1,2,3,4],[5,6],[7,8]]
 => [7,8,5,6,1,2,3,4] => ([(0,5),(1,4),(2,7),(6,3),(7,6)],8)
 => ? = 2
[4,2,1,1]
 => [[1,2,3,4],[5,6],[7],[8]]
 => [8,7,5,6,1,2,3,4] => ([(2,4),(3,5),(5,6),(6,7)],8)
 => ? = 2
[4,1,1,1,1]
 => [[1,2,3,4],[5],[6],[7],[8]]
 => [8,7,6,5,1,2,3,4] => ([(4,5),(5,7),(7,6)],8)
 => ? = 24
[3,3,2]
 => [[1,2,3],[4,5,6],[7,8]]
 => [7,8,4,5,6,1,2,3] => ([(0,5),(1,7),(2,6),(6,3),(7,4)],8)
 => ? = 2
[3,3,1,1]
 => [[1,2,3],[4,5,6],[7],[8]]
 => [8,7,4,5,6,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8)
 => ? = 4
[3,2,2,1]
 => [[1,2,3],[4,5],[6,7],[8]]
 => [8,6,7,4,5,1,2,3] => ([(1,5),(2,4),(3,6),(6,7)],8)
 => ? = 2
[3,2,1,1,1]
 => [[1,2,3],[4,5],[6],[7],[8]]
 => [8,7,6,4,5,1,2,3] => ([(3,5),(4,6),(6,7)],8)
 => ? = 6
[3,1,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,1,2,3] => ([(5,6),(6,7)],8)
 => ? = 120
[2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8)
 => ? = 24
[2,2,2,1,1]
 => [[1,2],[3,4],[5,6],[7],[8]]
 => [8,7,5,6,3,4,1,2] => ([(2,7),(3,6),(4,5)],8)
 => ? = 12
[2,2,1,1,1,1]
 => [[1,2],[3,4],[5],[6],[7],[8]]
 => [8,7,6,5,3,4,1,2] => ([(4,7),(5,6)],8)
 => ? = 48
[2,1,1,1,1,1,1]
 => [[1,2],[3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,3,1,2] => ([(6,7)],8)
 => ? = 720
[1,1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,3,2,1] => ([],8)
 => ? = 40320
[9]
 => [[1,2,3,4,5,6,7,8,9]]
 => [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 1
[8,1]
 => [[1,2,3,4,5,6,7,8],[9]]
 => [9,1,2,3,4,5,6,7,8] => ([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)
 => ? = 1
[7,2]
 => [[1,2,3,4,5,6,7],[8,9]]
 => [8,9,1,2,3,4,5,6,7] => ([(0,8),(1,3),(4,5),(5,7),(6,4),(7,2),(8,6)],9)
 => ? = 1
[7,1,1]
 => [[1,2,3,4,5,6,7],[8],[9]]
 => [9,8,1,2,3,4,5,6,7] => ([(2,8),(4,5),(5,7),(6,4),(7,3),(8,6)],9)
 => ? = 2
[6,3]
 => [[1,2,3,4,5,6],[7,8,9]]
 => [7,8,9,1,2,3,4,5,6] => ([(0,8),(1,7),(4,6),(5,4),(6,3),(7,5),(8,2)],9)
 => ? = 1
[6,2,1]
 => [[1,2,3,4,5,6],[7,8],[9]]
 => [9,7,8,1,2,3,4,5,6] => ([(1,8),(2,4),(5,7),(6,5),(7,3),(8,6)],9)
 => ? = 1
[6,1,1,1]
 => [[1,2,3,4,5,6],[7],[8],[9]]
 => [9,8,7,1,2,3,4,5,6] => ([(3,8),(5,7),(6,5),(7,4),(8,6)],9)
 => ? = 6
[5,4]
 => [[1,2,3,4,5],[6,7,8,9]]
 => [6,7,8,9,1,2,3,4,5] => ([(0,7),(1,8),(4,5),(5,2),(6,3),(7,6),(8,4)],9)
 => ? = 1
[5,3,1]
 => [[1,2,3,4,5],[6,7,8],[9]]
 => [9,6,7,8,1,2,3,4,5] => ([(1,8),(2,7),(5,6),(6,4),(7,5),(8,3)],9)
 => ? = 1
[5,2,2]
 => [[1,2,3,4,5],[6,7],[8,9]]
 => [8,9,6,7,1,2,3,4,5] => ([(0,5),(1,4),(2,8),(6,7),(7,3),(8,6)],9)
 => ? = 2
[5,2,1,1]
 => [[1,2,3,4,5],[6,7],[8],[9]]
 => [9,8,6,7,1,2,3,4,5] => ([(2,8),(3,5),(6,7),(7,4),(8,6)],9)
 => ? = 2
[5,1,1,1,1]
 => [[1,2,3,4,5],[6],[7],[8],[9]]
 => [9,8,7,6,1,2,3,4,5] => ([(4,5),(5,8),(7,6),(8,7)],9)
 => ? = 24
[4,4,1]
 => [[1,2,3,4],[5,6,7,8],[9]]
 => [9,5,6,7,8,1,2,3,4] => ([(1,8),(2,7),(5,3),(6,4),(7,5),(8,6)],9)
 => ? = 2
[4,3,2]
 => [[1,2,3,4],[5,6,7],[8,9]]
 => [8,9,5,6,7,1,2,3,4] => ([(0,5),(1,7),(2,8),(6,3),(7,4),(8,6)],9)
 => ? = 1
[4,3,1,1]
 => [[1,2,3,4],[5,6,7],[8],[9]]
 => [9,8,5,6,7,1,2,3,4] => ([(2,7),(3,8),(6,5),(7,6),(8,4)],9)
 => ? = 2
[4,2,2,1]
 => [[1,2,3,4],[5,6],[7,8],[9]]
 => [9,7,8,5,6,1,2,3,4] => ([(1,6),(2,5),(3,8),(7,4),(8,7)],9)
 => ? = 2
[4,2,1,1,1]
 => [[1,2,3,4],[5,6],[7],[8],[9]]
 => [9,8,7,5,6,1,2,3,4] => ([(3,5),(4,6),(6,7),(7,8)],9)
 => ? = 6
[4,1,1,1,1,1]
 => [[1,2,3,4],[5],[6],[7],[8],[9]]
 => [9,8,7,6,5,1,2,3,4] => ([(5,6),(6,8),(8,7)],9)
 => ? = 120
Description
The size of the automorphism group of a poset. A poset automorphism is a permutation of the elements of the poset preserving the order relation.