Identifier
-
Mp00306:
Posets
—rowmotion cycle type⟶
Integer partitions
St000474: Integer partitions ⟶ ℤ
Values
=>
Cc0014;cc-rep-0
Cc0002;cc-rep
([],1)=>[2]=>2
([],2)=>[2,2]=>2
([(0,1)],2)=>[3]=>3
([],3)=>[2,2,2,2]=>2
([(1,2)],3)=>[6]=>6
([(0,1),(0,2)],3)=>[3,2]=>3
([(0,2),(2,1)],3)=>[4]=>4
([(0,2),(1,2)],3)=>[3,2]=>3
([(2,3)],4)=>[6,6]=>6
([(1,2),(1,3)],4)=>[6,2,2]=>6
([(0,1),(0,2),(0,3)],4)=>[3,2,2,2]=>3
([(0,2),(0,3),(3,1)],4)=>[7]=>7
([(0,1),(0,2),(1,3),(2,3)],4)=>[4,2]=>4
([(1,2),(2,3)],4)=>[4,4]=>4
([(0,3),(3,1),(3,2)],4)=>[4,2]=>4
([(1,3),(2,3)],4)=>[6,2,2]=>6
([(0,3),(1,3),(3,2)],4)=>[4,2]=>4
([(0,3),(1,3),(2,3)],4)=>[3,2,2,2]=>3
([(0,3),(1,2)],4)=>[3,3,3]=>3
([(0,3),(1,2),(1,3)],4)=>[5,3]=>5
([(0,2),(0,3),(1,2),(1,3)],4)=>[3,2,2]=>3
([(0,3),(2,1),(3,2)],4)=>[5]=>5
([(0,3),(1,2),(2,3)],4)=>[7]=>7
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>[7,2,2]=>7
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>[4,2,2,2]=>4
([(0,3),(0,4),(4,1),(4,2)],5)=>[7,2,2]=>7
([(1,2),(1,3),(2,4),(3,4)],5)=>[4,4,2,2]=>4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>[5,2]=>5
([(0,3),(0,4),(3,2),(4,1)],5)=>[4,3,3]=>4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>[5,4]=>5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>[4,2,2]=>4
([(1,4),(4,2),(4,3)],5)=>[4,4,2,2]=>4
([(0,4),(4,1),(4,2),(4,3)],5)=>[4,2,2,2]=>4
([(1,4),(2,4),(4,3)],5)=>[4,4,2,2]=>4
([(0,4),(1,4),(4,2),(4,3)],5)=>[4,2,2]=>4
([(0,4),(1,4),(2,4),(4,3)],5)=>[4,2,2,2]=>4
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[5,3,2,2]=>5
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2,2,2,2]=>3
([(0,4),(1,4),(2,3),(4,2)],5)=>[5,2]=>5
([(0,4),(1,3),(2,3),(3,4)],5)=>[7,2,2]=>7
([(0,4),(1,2),(1,4),(2,3)],5)=>[8,3]=>8
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>[5,4]=>5
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>[7,2]=>7
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>[4,2,2]=>4
([(0,4),(1,2),(1,4),(4,3)],5)=>[10]=>10
([(0,2),(0,4),(3,1),(4,3)],5)=>[5,4]=>5
([(0,4),(1,2),(1,3),(3,4)],5)=>[10,2]=>10
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>[8]=>8
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[7,2,2]=>7
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>[5,3,2,2]=>5
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>[3,2,2,2,2]=>3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>[10]=>10
([(0,3),(1,2),(1,4),(3,4)],5)=>[8,3]=>8
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>[7,2]=>7
([(1,4),(3,2),(4,3)],5)=>[10]=>10
([(0,3),(3,4),(4,1),(4,2)],5)=>[5,2]=>5
([(0,4),(1,2),(2,4),(4,3)],5)=>[8]=>8
([(0,3),(1,4),(4,2)],5)=>[12]=>12
([(0,4),(3,2),(4,1),(4,3)],5)=>[8]=>8
([(0,4),(1,2),(2,3),(2,4)],5)=>[10]=>10
([(0,4),(2,3),(3,1),(4,2)],5)=>[6]=>6
([(0,3),(1,2),(2,4),(3,4)],5)=>[4,3,3]=>4
([(0,4),(1,2),(2,3),(3,4)],5)=>[5,4]=>5
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>[5,2]=>5
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>[5,2,2,2]=>5
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2,2,2,2]=>4
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>[8,2,2]=>8
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>[5,2,2]=>5
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>[8,2]=>8
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>[5,2,2]=>5
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)=>[11]=>11
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[4,2,2,2,2]=>4
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>[5,2,2,2]=>5
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>[4,2,2,2,2]=>4
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>[4,2,2,2,2]=>4
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>[5,2,2,2]=>5
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>[4,2,2,2,2]=>4
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>[8,2,2]=>8
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>[8,2]=>8
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>[5,2,2]=>5
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>[5,3,3]=>5
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>[8,2,2]=>8
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>[6,2]=>6
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>[8,2,2]=>8
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>[5,2,2,2]=>5
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>[5,2,2]=>5
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>[5,4,2]=>5
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>[5,5]=>5
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>[8,4]=>8
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)=>[4,3,3,2]=>4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>[5,4,2]=>5
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>[4,2,2,2]=>4
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>[5,4,2]=>5
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>[5,2,2]=>5
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>[8,2]=>8
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>[9,3]=>9
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>[5,5]=>5
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)=>[9,3]=>9
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>[11]=>11
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>[9]=>9
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>[8,2,2]=>8
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>[6,4]=>6
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>[6,2]=>6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>[4,2,2,2,2]=>4
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>[7,5]=>7
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>[11]=>11
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>[8,4]=>8
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>[8,2]=>8
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)=>[11]=>11
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>[11]=>11
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>[8,2]=>8
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>[9,3]=>9
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>[11]=>11
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>[8,2,2]=>8
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>[7,5]=>7
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>[8,2]=>8
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>[6,6]=>6
([(1,5),(3,4),(4,2),(5,3)],6)=>[6,6]=>6
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>[6,2]=>6
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>[5,3,3]=>5
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>[6,4]=>6
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)=>[4,3,3,2]=>4
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>[6,2]=>6
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>[6,4]=>6
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>[9,3]=>9
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)=>[11]=>11
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>[7,5]=>7
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>[5,4,2]=>5
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>[5,2,2]=>5
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>[5,5]=>5
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)=>[5,3,3]=>5
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)=>[11]=>11
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>[9]=>9
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>[7,5]=>7
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>[7]=>7
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>[9]=>9
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>[11]=>11
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>[6,2]=>6
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>[9]=>9
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)=>[6,2,2]=>6
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)=>[5,5,2]=>5
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>[5,2,2,2]=>5
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)=>[9,2]=>9
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>[6,2,2,2]=>6
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>[6,2,2,2]=>6
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)=>[9,2]=>9
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>[12]=>12
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)=>[6,2,2]=>6
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>[6,2,2]=>6
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)=>[6,4,2]=>6
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)=>[6,2,2]=>6
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>[12]=>12
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>[7,2]=>7
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>[7,2]=>7
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)=>[6,2,2]=>6
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)=>[5,5,2]=>5
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)=>[5,2,2,2]=>5
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)=>[5,5,2]=>5
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>[5,2,2,2]=>5
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)=>[9,2]=>9
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>[9,2]=>9
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)=>[5,5,2]=>5
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>[8,2,2]=>8
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)=>[5,2,2,2]=>5
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)=>[8,2,2]=>8
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)=>[6,2,2]=>6
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)=>[9,2]=>9
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)=>[6,4,2]=>6
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>[6,2,2,2]=>6
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)=>[5,5,2]=>5
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>[6,5]=>6
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)=>[12]=>12
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>[7,4]=>7
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)=>[6,4,2]=>6
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>[7,2]=>7
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)=>[9,2]=>9
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)=>[6,4,2]=>6
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)=>[9,2]=>9
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>[6,3,3]=>6
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)=>[12]=>12
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)=>[9,2]=>9
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>[12]=>12
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)=>[6,2,2]=>6
([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>[8,2,2]=>8
([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7)=>[12]=>12
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>[6,5]=>6
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>[6,4,2]=>6
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)=>[9,2]=>9
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)=>[6,2,2]=>6
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)=>[6,2,2]=>6
([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)=>[12]=>12
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>[6,2,2,2]=>6
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)=>[6,2,2,2]=>6
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>[10]=>10
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)=>[6,4,2]=>6
([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)=>[12]=>12
([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>[5,5,2]=>5
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)=>[6,5]=>6
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>[12]=>12
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>[10]=>10
([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7)=>[12]=>12
([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)=>[12]=>12
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)=>[9,2]=>9
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)=>[12]=>12
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)=>[9,2]=>9
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)=>[6,2,2]=>6
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)=>[6,5]=>6
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)=>[9,2]=>9
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)=>[7,2]=>7
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)=>[7,4]=>7
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)=>[12]=>12
([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7)=>[12]=>12
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)=>[12]=>12
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)=>[6,3,3]=>6
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)=>[10]=>10
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>[8]=>8
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>[10]=>10
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>[10]=>10
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>[6,3,3]=>6
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)=>[6,3,3]=>6
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>[7,2]=>7
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>[7,4]=>7
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>[7,2]=>7
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>[7,4]=>7
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)=>[7,5]=>7
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Description
Dyson's crank of a partition.
Let $\lambda$ be a partition and let $o(\lambda)$ be the number of parts that are equal to 1 (St000475The number of parts equal to 1 in a partition.), and let $\mu(\lambda)$ be the number of parts that are strictly larger than $o(\lambda)$ (St000473The number of parts of a partition that are strictly bigger than the number of ones.). Dyson's crank is then defined as
$$crank(\lambda) = \begin{cases} \text{ largest part of }\lambda & o(\lambda) = 0\\ \mu(\lambda) - o(\lambda) & o(\lambda) > 0. \end{cases}$$
Let $\lambda$ be a partition and let $o(\lambda)$ be the number of parts that are equal to 1 (St000475The number of parts equal to 1 in a partition.), and let $\mu(\lambda)$ be the number of parts that are strictly larger than $o(\lambda)$ (St000473The number of parts of a partition that are strictly bigger than the number of ones.). Dyson's crank is then defined as
$$crank(\lambda) = \begin{cases} \text{ largest part of }\lambda & o(\lambda) = 0\\ \mu(\lambda) - o(\lambda) & o(\lambda) > 0. \end{cases}$$
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.
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