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Your data matches 10 different statistics following compositions of up to 3 maps.
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Matching statistic: St000706
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
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
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%
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]
=> [[[[[[[[[]]]]]]]]]
=> ? ∊ {1,1,2,6,24}
[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]
=> [[[[[[[[]]]]]]],[]]
=> ? ∊ {1,1,2,6,24}
[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]
=> [[[[[[[]]]]]],[],[]]
=> ? ∊ {1,1,2,6,24}
[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]
=> [[[[[[]]]]],[],[],[]]
=> ? ∊ {1,1,2,6,24}
[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]
=> [[[[[]]]],[],[],[],[]]
=> ? ∊ {1,1,2,6,24}
[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]
=> [[[[[[[[[[]]]]]]]]]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[[[[]]]]]]]],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[[[]]]]]],[]]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[[[]]]]]]],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[[]]]]],[]],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[[]]]]]],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[]]]],[]],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[]]]]],[],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[]]],[]],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[]]]],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[]],[]],[],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[]]],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[]],[],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[],[],[],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,2,2,6,6,24,24,120,720,5040,362880}
[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]
=> [[[[[[[[[[[]]]]]]]]]]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[[[[]]]]]]]]],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[[[]]]]]]],[]]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[[[]]]]]]]],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[[]]]]],[]]]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[[]]]]]],[]],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[[]]]]]]],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[]]]],[]]],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[]]]]],[],[]]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[]]]]],[]],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[]]]]]],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[]]],[]]],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[]]]],[],[]],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[]]]],[]],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[]]]]],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[]],[]]],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[]]],[],[]],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[]]],[]],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[]]]],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[],[]]],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[]],[],[]],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[]],[]],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[]]],[],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[],[],[]],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[],[]],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[]],[],[],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[],[],[],[],[],[],[],[],[],[]]
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,4,6,6,6,12,24,24,48,120,120,144,720,1440,5040,40320,3628800}
[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]
=> [[[[[[[[[[[[]]]]]]]]]]]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,6,12,12,12,12,24,24,24,48,120,120,144,240,720,720,720,5040,10080,40320,362880,39916800}
[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]
=> [[[[[[[[[[[]]]]]]]]]],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,6,12,12,12,12,24,24,24,48,120,120,144,240,720,720,720,5040,10080,40320,362880,39916800}
[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]
=> [[[[[[[[[[]]]]]]]],[]]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,6,12,12,12,12,24,24,24,48,120,120,144,240,720,720,720,5040,10080,40320,362880,39916800}
[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]
=> [[[[[[[[[[]]]]]]]]],[],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,6,12,12,12,12,24,24,24,48,120,120,144,240,720,720,720,5040,10080,40320,362880,39916800}
Description
The size of the automorphism group of the ordered tree.
Matching statistic: St000260
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 8% ●values known / values provided: 19%●distinct values known / distinct values provided: 8%
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 8% ●values known / values provided: 19%●distinct values known / distinct values provided: 8%
Values
[2]
=> [1,0,1,0]
=> [1,2] => ([],2)
=> ? = 2
[1,1]
=> [1,1,0,0]
=> [2,1] => ([(0,1)],2)
=> 1
[3]
=> [1,0,1,0,1,0]
=> [1,2,3] => ([],3)
=> ? ∊ {1,6}
[2,1]
=> [1,0,1,1,0,0]
=> [1,3,2] => ([(1,2)],3)
=> ? ∊ {1,6}
[1,1,1]
=> [1,1,0,1,0,0]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> 1
[4]
=> [1,0,1,0,1,0,1,0]
=> [1,2,3,4] => ([],4)
=> ? ∊ {2,2,24}
[3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {2,2,24}
[2,2]
=> [1,1,1,0,0,0]
=> [3,1,2] => ([(0,2),(1,2)],3)
=> 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {2,2,24}
[1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => ([],5)
=> ? ∊ {1,1,2,6,120}
[4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => ([(3,4)],5)
=> ? ∊ {1,1,2,6,120}
[3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {1,1,2,6,120}
[3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,2,6,120}
[2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,2,6,120}
[1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => ([],6)
=> ? ∊ {1,1,4,6,6,24,720}
[5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => ([(4,5)],6)
=> ? ∊ {1,1,4,6,6,24,720}
[4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,4,6,6,24,720}
[4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => ([(3,5),(4,5)],6)
=> ? ∊ {1,1,4,6,6,24,720}
[3,3]
=> [1,1,1,0,1,0,0,0]
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {1,1,4,6,6,24,720}
[3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,4,6,6,24,720}
[2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 1
[2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,4,6,6,24,720}
[1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
[7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6,7] => ([],7)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,5,7,6] => ([(5,6)],7)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,6,4,5] => ([(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[5,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[2,2,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 2
[2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,2,6,6,12,24,120,5040}
[1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1
[8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6,7,8] => ([],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[7,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,5,6,8,7] => ([(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[6,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,4,7,5,6] => ([(4,6),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[6,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,4,5,7,8,6] => ([(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[5,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,2,3,6,4,7,5] => ([(3,6),(4,5),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[5,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,3,4,6,7,8,5] => ([(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,2,5,3,6,7,4] => ([(2,6),(3,6),(4,5),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[4,1,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,3,5,6,7,8,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[3,2,1,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,4,2,5,6,7,3] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[3,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,2,4,5,6,7,8,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[2,2,2,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 2
[2,2,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [3,1,4,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> 2
[2,1,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,4,5,6,7,8,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,4,6,6,12,24,24,48,120,720,40320}
[9]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6,7,8,9] => ([],9)
=> ? ∊ {1,1,1,1,1,1,1,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[8,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,5,6,7,9,8] => ([(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[7,2]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,4,5,8,6,7] => ([(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[7,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,4,5,6,8,9,7] => ([(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[6,3]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7)
=> ? ∊ {1,1,1,1,1,1,1,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[4,4,1]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
[3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 2
[3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [3,4,1,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[2,2,2,2,1]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[2,2,2,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=> [4,1,2,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> 2
[5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
[4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [3,4,5,1,6,7,2] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[3,3,3,1]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> 2
[3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
[3,3,2,1,1]
=> [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [3,5,1,2,6,7,4] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
=> 2
[2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [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)
=> 2
[2,2,2,2,1,1]
=> [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [4,5,1,2,6,7,3] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[5,5,1]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [3,4,5,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[4,4,2,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=> [3,4,6,1,2,7,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> 2
[3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
[3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> 2
[3,3,2,2,1]
=> [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [3,5,6,1,2,7,4] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
[2,2,2,2,2,1]
=> [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=> [4,5,6,1,2,7,3] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> 2
[6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[5,5,2]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [3,4,5,7,1,2,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
[4,4,3,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [3,6,1,2,4,7,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
=> 2
[4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [3,4,6,7,1,2,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[3,3,3,3]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1
[3,3,3,2,1]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [5,1,6,2,3,7,4] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[3,3,2,2,2]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [3,5,6,7,1,2,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 2
[2,2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [4,5,6,7,1,2,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St001491
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00200: Binary words —twist⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 8% ●values known / values provided: 13%●distinct values known / distinct values provided: 8%
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00200: Binary words —twist⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 8% ●values known / values provided: 13%●distinct values known / distinct values provided: 8%
Values
[2]
=> []
=> => ? => ? ∊ {1,2}
[1,1]
=> [1]
=> 10 => 00 => ? ∊ {1,2}
[3]
=> []
=> => ? => ? ∊ {1,6}
[2,1]
=> [1]
=> 10 => 00 => ? ∊ {1,6}
[1,1,1]
=> [1,1]
=> 110 => 010 => 1
[4]
=> []
=> => ? => ? ∊ {1,2,24}
[3,1]
=> [1]
=> 10 => 00 => ? ∊ {1,2,24}
[2,2]
=> [2]
=> 100 => 000 => ? ∊ {1,2,24}
[2,1,1]
=> [1,1]
=> 110 => 010 => 1
[1,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[5]
=> []
=> => ? => ? ∊ {1,2,6,120}
[4,1]
=> [1]
=> 10 => 00 => ? ∊ {1,2,6,120}
[3,2]
=> [2]
=> 100 => 000 => ? ∊ {1,2,6,120}
[3,1,1]
=> [1,1]
=> 110 => 010 => 1
[2,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[2,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[1,1,1,1,1]
=> [1,1,1,1]
=> 11110 => 01110 => ? ∊ {1,2,6,120}
[6]
=> []
=> => ? => ? ∊ {1,2,4,6,6,24,720}
[5,1]
=> [1]
=> 10 => 00 => ? ∊ {1,2,4,6,6,24,720}
[4,2]
=> [2]
=> 100 => 000 => ? ∊ {1,2,4,6,6,24,720}
[4,1,1]
=> [1,1]
=> 110 => 010 => 1
[3,3]
=> [3]
=> 1000 => 0000 => ? ∊ {1,2,4,6,6,24,720}
[3,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[3,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[2,2,2]
=> [2,2]
=> 1100 => 0100 => 1
[2,2,1,1]
=> [2,1,1]
=> 10110 => 00110 => ? ∊ {1,2,4,6,6,24,720}
[2,1,1,1,1]
=> [1,1,1,1]
=> 11110 => 01110 => ? ∊ {1,2,4,6,6,24,720}
[1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 111110 => 011110 => ? ∊ {1,2,4,6,6,24,720}
[7]
=> []
=> => ? => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[6,1]
=> [1]
=> 10 => 00 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[5,2]
=> [2]
=> 100 => 000 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[5,1,1]
=> [1,1]
=> 110 => 010 => 1
[4,3]
=> [3]
=> 1000 => 0000 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[4,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[4,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[3,3,1]
=> [3,1]
=> 10010 => 00010 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[3,2,2]
=> [2,2]
=> 1100 => 0100 => 1
[3,2,1,1]
=> [2,1,1]
=> 10110 => 00110 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[3,1,1,1,1]
=> [1,1,1,1]
=> 11110 => 01110 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[2,2,2,1]
=> [2,2,1]
=> 11010 => 01010 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[2,2,1,1,1]
=> [2,1,1,1]
=> 101110 => 001110 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[2,1,1,1,1,1]
=> [1,1,1,1,1]
=> 111110 => 011110 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> 1111110 => 0111110 => ? ∊ {1,1,2,2,2,6,6,12,24,120,5040}
[8]
=> []
=> => ? => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[7,1]
=> [1]
=> 10 => 00 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,2]
=> [2]
=> 100 => 000 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,1,1]
=> [1,1]
=> 110 => 010 => 1
[5,3]
=> [3]
=> 1000 => 0000 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[5,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[4,4]
=> [4]
=> 10000 => 00000 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,3,1]
=> [3,1]
=> 10010 => 00010 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,2,2]
=> [2,2]
=> 1100 => 0100 => 1
[4,2,1,1]
=> [2,1,1]
=> 10110 => 00110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,1,1,1,1]
=> [1,1,1,1]
=> 11110 => 01110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,3,2]
=> [3,2]
=> 10100 => 00100 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,3,1,1]
=> [3,1,1]
=> 100110 => 000110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,2,2,1]
=> [2,2,1]
=> 11010 => 01010 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,2,1,1,1]
=> [2,1,1,1]
=> 101110 => 001110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,1,1,1,1,1]
=> [1,1,1,1,1]
=> 111110 => 011110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,2,2,2]
=> [2,2,2]
=> 11100 => 01100 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,2,2,1,1]
=> [2,2,1,1]
=> 110110 => 010110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,2,1,1,1,1]
=> [2,1,1,1,1]
=> 1011110 => 0011110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> 1111110 => 0111110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 11111110 => 01111110 => ? ∊ {1,1,1,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[9]
=> []
=> => ? => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[8,1]
=> [1]
=> 10 => 00 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[7,2]
=> [2]
=> 100 => 000 => ? ∊ {1,1,1,1,1,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[7,1,1]
=> [1,1]
=> 110 => 010 => 1
[6,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[6,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[5,2,2]
=> [2,2]
=> 1100 => 0100 => 1
[8,1,1]
=> [1,1]
=> 110 => 010 => 1
[7,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[7,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[6,2,2]
=> [2,2]
=> 1100 => 0100 => 1
[9,1,1]
=> [1,1]
=> 110 => 010 => 1
[8,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[8,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[7,2,2]
=> [2,2]
=> 1100 => 0100 => 1
[10,1,1]
=> [1,1]
=> 110 => 010 => 1
[9,2,1]
=> [2,1]
=> 1010 => 0010 => 1
[9,1,1,1]
=> [1,1,1]
=> 1110 => 0110 => 2
[8,2,2]
=> [2,2]
=> 1100 => 0100 => 1
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let An=K[x]/(xn).
We associate to a nonempty subset S of an (n-1)-set the module MS, which is the direct sum of An-modules with indecomposable non-projective direct summands of dimension i when i is in S (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of MS. We decode the subset as a binary word so that for example the subset S={1,3} of {1,2,3} is decoded as 101.
Matching statistic: St000633
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%
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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
[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)
=> ? ∊ {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,4,6,6,6,6,12,24,24,24,36,120,240,720,5040,362880}
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.
Matching statistic: St000782
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St000782: Perfect matchings ⟶ ℤResult quality: 4% ●values known / values provided: 11%●distinct values known / distinct values provided: 4%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St000782: Perfect matchings ⟶ ℤResult quality: 4% ●values known / values provided: 11%●distinct values known / distinct values provided: 4%
Values
[2]
=> []
=> []
=> []
=> ? ∊ {1,2}
[1,1]
=> [1]
=> [1,0]
=> [(1,2)]
=> ? ∊ {1,2}
[3]
=> []
=> []
=> []
=> ? ∊ {1,1,6}
[2,1]
=> [1]
=> [1,0]
=> [(1,2)]
=> ? ∊ {1,1,6}
[1,1,1]
=> [1,1]
=> [1,1,0,0]
=> [(1,4),(2,3)]
=> ? ∊ {1,1,6}
[4]
=> []
=> []
=> []
=> ? ∊ {1,2,2,24}
[3,1]
=> [1]
=> [1,0]
=> [(1,2)]
=> ? ∊ {1,2,2,24}
[2,2]
=> [2]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> ? ∊ {1,2,2,24}
[2,1,1]
=> [1,1]
=> [1,1,0,0]
=> [(1,4),(2,3)]
=> ? ∊ {1,2,2,24}
[1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[5]
=> []
=> []
=> []
=> ? ∊ {1,2,2,6,120}
[4,1]
=> [1]
=> [1,0]
=> [(1,2)]
=> ? ∊ {1,2,2,6,120}
[3,2]
=> [2]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> ? ∊ {1,2,2,6,120}
[3,1,1]
=> [1,1]
=> [1,1,0,0]
=> [(1,4),(2,3)]
=> ? ∊ {1,2,2,6,120}
[2,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[2,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> ? ∊ {1,2,2,6,120}
[6]
=> []
=> []
=> []
=> ? ∊ {2,2,4,6,6,24,720}
[5,1]
=> [1]
=> [1,0]
=> [(1,2)]
=> ? ∊ {2,2,4,6,6,24,720}
[4,2]
=> [2]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> ? ∊ {2,2,4,6,6,24,720}
[4,1,1]
=> [1,1]
=> [1,1,0,0]
=> [(1,4),(2,3)]
=> ? ∊ {2,2,4,6,6,24,720}
[3,3]
=> [3]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> 1
[3,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[3,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[2,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> 1
[2,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> ? ∊ {2,2,4,6,6,24,720}
[2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> ? ∊ {2,2,4,6,6,24,720}
[1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [(1,10),(2,3),(4,5),(6,7),(8,9)]
=> ? ∊ {2,2,4,6,6,24,720}
[7]
=> []
=> []
=> []
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[6,1]
=> [1]
=> [1,0]
=> [(1,2)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[5,2]
=> [2]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[5,1,1]
=> [1,1]
=> [1,1,0,0]
=> [(1,4),(2,3)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[4,3]
=> [3]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> 1
[4,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[4,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[3,3,1]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[3,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> 1
[3,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[3,1,1,1,1]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[2,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [(1,8),(2,5),(3,4),(6,7)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[2,2,1,1,1]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[2,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [(1,10),(2,3),(4,5),(6,7),(8,9)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]
=> ? ∊ {1,2,2,2,2,6,6,12,24,120,5040}
[8]
=> []
=> []
=> []
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[7,1]
=> [1]
=> [1,0]
=> [(1,2)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,2]
=> [2]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,1,1]
=> [1,1]
=> [1,1,0,0]
=> [(1,4),(2,3)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,3]
=> [3]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> 1
[5,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[5,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[4,4]
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,3,1]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> 1
[4,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,1,1,1,1]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,3,2]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,3,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,10),(6,7),(8,9)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [(1,8),(2,5),(3,4),(6,7)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,2,1,1,1]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[3,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [(1,10),(2,3),(4,5),(6,7),(8,9)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,2,2,2]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [(1,8),(2,7),(3,6),(4,5)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,2,2,1,1]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [(1,10),(2,5),(3,4),(6,7),(8,9)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,2,1,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[2,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [(1,14),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]
=> ? ∊ {1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,3]
=> [3]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> 1
[6,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[6,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[5,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> 1
[7,3]
=> [3]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> 1
[7,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[7,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[6,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> 1
[8,3]
=> [3]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> 1
[8,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[8,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[7,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> 1
[9,3]
=> [3]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> 1
[9,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> 1
[9,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> 1
[8,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> 1
Description
The indicator function of whether a given perfect matching is an L & P matching.
An L&P matching is built inductively as follows:
starting with either a single edge, or a hairpin ([1,3],[2,4]), insert a noncrossing matching or inflate an edge by a ladder, that is, a number of nested edges.
The number of L&P matchings is (see [thm. 1, 2])
\frac{1}{2} \cdot 4^{n} + \frac{1}{n + 1}{2 \, n \choose n} - {2 \, n + 1 \choose n} + {2 \, n - 1 \choose n - 1}
Matching statistic: St001630
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 9%●distinct values known / distinct values provided: 8%
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 9%●distinct values known / distinct values provided: 8%
Values
[2]
=> [1,1,0,0,1,0]
=> [[2,2],[1]]
=> ([],1)
=> ? ∊ {1,2}
[1,1]
=> [1,0,1,1,0,0]
=> [[2,1],[]]
=> ([],1)
=> ? ∊ {1,2}
[3]
=> [1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> ([],1)
=> ? ∊ {1,1,6}
[2,1]
=> [1,0,1,0,1,0]
=> [[1,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,6}
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,6}
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,24}
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [[3,3,3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,2,2,6,120}
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [[4,4,4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [[4,4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[4,4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [[4,4,4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [[4,4,4,4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [[3,3,3,3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [[3,3,3,3],[2,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [[3,3,3,2],[2]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [[3,3,3,3,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [[4,4,4,4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> [[5,5,5,5,5],[4]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[7,1]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
=> [[5,5,5,5],[4]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=> [[4,4,4,3],[3]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,1,1]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [[4,4,4,4],[3,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [[4,4,3],[3]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,2,1]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [[2,2,2,2,2],[1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,1,1,1]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [[4,4,4],[3,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,2,2]
=> [1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,1,1,1]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[6,2,2]
=> [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> [[4,4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,3,1,1]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,4,2]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[4,4,1,1]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,2,2,2]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,2,2]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[3,3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [[4,4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,3,3]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[5,3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[5,2,2,2]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,3,3,1]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,3,1,1]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[5,3,3,1]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 1
[5,3,2,2]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[4,4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001878
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 9%●distinct values known / distinct values provided: 8%
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 8% ●values known / values provided: 9%●distinct values known / distinct values provided: 8%
Values
[2]
=> [1,1,0,0,1,0]
=> [[2,2],[1]]
=> ([],1)
=> ? ∊ {1,2}
[1,1]
=> [1,0,1,1,0,0]
=> [[2,1],[]]
=> ([],1)
=> ? ∊ {1,2}
[3]
=> [1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> ([],1)
=> ? ∊ {1,1,6}
[2,1]
=> [1,0,1,0,1,0]
=> [[1,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,6}
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,6}
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,24}
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> ([],1)
=> ? ∊ {1,1,2,2,24}
[5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [[3,3,3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,2,2,6,120}
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,2,2,6,120}
[6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [[4,4,4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [[4,4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[4,4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [[4,4,4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,4,6,6,24,720}
[7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [[4,4,4,4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [[3,3,3,3,3],[2]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [[3,3,3,3],[2,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [[3,3,3,2],[2]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3,1],[1]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [[3,3,3,3,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [[4,4,4,4,1],[]]
=> ([],1)
=> ? ∊ {1,1,1,1,1,2,2,2,2,6,6,12,24,120,5040}
[8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> [[5,5,5,5,5],[4]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[7,1]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
=> [[5,5,5,5],[4]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=> [[4,4,4,3],[3]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[6,1,1]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [[4,4,4,4],[3,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [[4,4,3],[3]]
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,2,1]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [[2,2,2,2,2],[1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[5,1,1,1]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [[4,4,4],[3,1]]
=> ([],1)
=> ? ∊ {1,1,1,1,2,2,2,2,2,2,4,6,6,12,24,24,48,120,720,40320}
[4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,2,2]
=> [1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,1,1,1]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[6,2,2]
=> [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> [[4,4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,3,1,1]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,4,2]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[4,4,1,1]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,2,2,2]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,2,2]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[3,3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [[4,4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,3,3]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[5,3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[5,2,2,2]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> 1
[5,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
[4,3,3,1]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 1
[3,3,3,1,1]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[5,3,3,1]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 1
[5,3,2,2]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[4,4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St001198
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 8%●distinct values known / distinct values provided: 4%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 8%●distinct values known / distinct values provided: 4%
Values
[2]
=> [1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {1,2}
[1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {1,2}
[3]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,6}
[2,1]
=> [1,0,1,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,6}
[1,1,1]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,6}
[4]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,2,2,24}
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[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]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[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]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[5,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[2,2,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[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]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[7,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[6,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[6,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[5,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[5,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 2
[4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 2
[2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[2,2,2,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 2
[4,3,2]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 2
[3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2
[3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 2
[3,2,2,2]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[2,2,2,2,1]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 2
[4,3,3]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 2
[3,3,3,1]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> 2
[3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 2
[3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> 2
[4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> 2
[3,3,3,3]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> 2
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
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 8%●distinct values known / distinct values provided: 4%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 8%●distinct values known / distinct values provided: 4%
Values
[2]
=> [1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {1,2}
[1,1]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? ∊ {1,2}
[3]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,6}
[2,1]
=> [1,0,1,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,6}
[1,1,1]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,6}
[4]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[2,2]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? ∊ {1,1,2,2,24}
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,2,2,24}
[5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[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]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,2,2,6,120}
[6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[4,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[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]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,2,4,6,6,24,720}
[7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[5,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[4,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 2
[2,2,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[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]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,2,2,6,6,12,24,120,5040}
[8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[7,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[6,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[6,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[5,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[5,1,1,1]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[4,3,1]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 2
[4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,2,4,6,6,12,24,24,48,120,720,40320}
[3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 2
[2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[2,2,2,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 2
[4,3,2]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 2
[3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2
[3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 2
[3,2,2,2]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[2,2,2,2,1]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 2
[4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 2
[4,3,3]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 2
[3,3,3,1]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> 2
[3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 2
[3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> 2
[4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> 2
[3,3,3,3]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> 2
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.
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