Identifier
-
Mp00307:
Posets
—promotion cycle type⟶
Integer partitions
St000143: Integer partitions ⟶ ℤ
Values
([],1) => [1] => 0
([],2) => [2] => 0
([(0,1)],2) => [1] => 0
([],3) => [3,3] => 3
([(1,2)],3) => [3] => 0
([(0,1),(0,2)],3) => [2] => 0
([(0,2),(2,1)],3) => [1] => 0
([(0,2),(1,2)],3) => [2] => 0
([(1,2),(1,3)],4) => [8] => 0
([(0,1),(0,2),(0,3)],4) => [3,3] => 3
([(0,2),(0,3),(3,1)],4) => [3] => 0
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => 0
([(1,2),(2,3)],4) => [4] => 0
([(0,3),(3,1),(3,2)],4) => [2] => 0
([(1,3),(2,3)],4) => [8] => 0
([(0,3),(1,3),(3,2)],4) => [2] => 0
([(0,3),(1,3),(2,3)],4) => [3,3] => 3
([(0,3),(1,2)],4) => [4,2] => 0
([(0,3),(1,2),(1,3)],4) => [3,2] => 0
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => 2
([(0,3),(2,1),(3,2)],4) => [1] => 0
([(0,3),(1,2),(2,3)],4) => [3] => 0
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => [8] => 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,3] => 3
([(0,3),(0,4),(4,1),(4,2)],5) => [8] => 0
([(1,2),(1,3),(2,4),(3,4)],5) => [5,5] => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => 0
([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => 0
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => 2
([(1,4),(4,2),(4,3)],5) => [5,5] => 5
([(0,4),(4,1),(4,2),(4,3)],5) => [3,3] => 3
([(1,4),(2,4),(4,3)],5) => [5,5] => 5
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => 2
([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => 3
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => 0
([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 0
([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => 0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => 0
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [6] => 0
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => 2
([(0,4),(1,2),(1,4),(4,3)],5) => [7] => 0
([(0,2),(0,4),(3,1),(4,3)],5) => [4] => 0
([(0,4),(1,2),(1,3),(3,4)],5) => [4,4,3] => 4
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [8] => 0
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [5,3] => 0
([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => 0
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [6] => 0
([(1,4),(3,2),(4,3)],5) => [5] => 0
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => 0
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 0
([(0,3),(1,4),(4,2)],5) => [5,5] => 5
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => 0
([(0,4),(1,2),(2,3),(2,4)],5) => [7] => 0
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => 0
([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => 0
([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [3,3] => 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => [8] => 0
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => [5,5] => 5
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [6] => 0
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => [7] => 0
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [3,3] => 3
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => 3
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 0
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [6] => 0
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => 2
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => [5,5] => 5
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => 0
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => [8] => 0
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => 0
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [8] => 0
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,5] => 5
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [3,3] => 3
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 5
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => 2
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [6,2,2] => 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [3,2] => 0
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => [4,4,2,2] => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [6,2,2] => 2
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [2,2,2,2] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [4,4] => 4
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [6] => 0
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => [5,5] => 5
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => [5,5] => 5
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => 0
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => 0
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => [5,4] => 0
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => [5,3] => 0
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => 0
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [8] => 0
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => [4,4,3] => 4
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => [4,4,3] => 4
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [4] => 0
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [5,5] => 5
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Description
The largest repeated part of a partition.
If the parts of the partition are all distinct, the value of the statistic is defined to be zero.
If the parts of the partition are all distinct, the value of the statistic is defined to be zero.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.
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