Your data matches 45 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Mp00198: Posets incomparability graphGraphs
Mp00156: Graphs line graphGraphs
Mp00111: Graphs complementGraphs
St000456: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2)],4)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,4),(2,3)],5)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(1,4),(2,3)],5)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 3
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 1
([(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
=> 2
([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(1,4),(2,3)],5)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,4),(1,2),(1,3)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 3
([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,1),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,3),(1,4),(4,2)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
=> 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> ([(2,5),(3,4)],6)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ([(1,2),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> ([],2)
=> ([(0,1)],2)
=> 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> 3
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> ([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> 5
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 3
Description
The monochromatic index of a connected graph. This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path. For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Mp00307: Posets promotion cycle typeInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
St001227: Dyck paths ⟶ ℤResult quality: 12% values known / values provided: 12%distinct values known / distinct values provided: 33%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 3 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 3 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 3 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 3 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ? = 5 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> ? = 1 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,4,4,4,4,4,4,4,4,4,4]
=> ?
=> ? = 4 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4 = 3 + 1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 4 = 3 + 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4 = 3 + 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 4 = 3 + 1
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 4 = 3 + 1
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St001225
Mp00307: Posets promotion cycle typeInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00132: Dyck paths switch returns and last double riseDyck paths
St001225: Dyck paths ⟶ ℤResult quality: 12% values known / values provided: 12%distinct values known / distinct values provided: 33%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 3 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 3 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 3 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 3 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 5 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
=> ? = 1 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,4,4,4,4,4,4,4,4,4,4]
=> ?
=> ?
=> ? = 4 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 1 + 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> 4 = 3 + 1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4 = 3 + 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> 4 = 3 + 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4 = 3 + 1
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4 = 3 + 1
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 2 = 1 + 1
Description
The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St001480
Mp00307: Posets promotion cycle typeInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00101: Dyck paths decomposition reverseDyck paths
St001480: Dyck paths ⟶ ℤResult quality: 12% values known / values provided: 12%distinct values known / distinct values provided: 33%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 5 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,4,4,4,4,4,4,4,4,4,4]
=> ?
=> ?
=> ? = 4 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> 3 = 2 + 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> 2 = 1 + 1
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2 = 1 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 2 = 1 + 1
Description
The number of simple summands of the module J^2/J^3. Here J is the Jacobson radical of the Nakayama algebra algebra corresponding to the Dyck path.
Matching statistic: St001291
Mp00307: Posets promotion cycle typeInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00028: Dyck paths reverseDyck paths
St001291: Dyck paths ⟶ ℤResult quality: 12% values known / values provided: 12%distinct values known / distinct values provided: 33%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 2
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 2
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 5 + 2
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
=> ? = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ?
=> ? = 3 + 2
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ?
=> ? = 2 + 2
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 3 + 2
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
=> [1,0,1,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 2 + 2
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,4,4,4,4,4,4,4,4,4,4]
=> ?
=> ?
=> ? = 4 + 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 4 = 2 + 2
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
=> [2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7)
=> [4,4,2,2]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 5 = 3 + 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
=> [5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> [4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> [3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 4 = 2 + 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7)
=> [5,4]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 3 = 1 + 2
Description
The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. Let $A$ be the Nakayama algebra associated to a Dyck path as given in [[DyckPaths/NakayamaAlgebras]]. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Matching statistic: St001934
Mp00307: Posets promotion cycle typeInteger partitions
Mp00044: Integer partitions conjugateInteger partitions
St001934: Integer partitions ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 11%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2,2]
=> 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2,2]
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2,2]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> ? = 3
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> ? = 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [2,2,2,2,1]
=> ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [4,4,4,4,4]
=> ? = 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2,2]
=> 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> ? = 3
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> ? = 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [2,2,2,1,1]
=> ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [2,2,2,2,1]
=> ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [2,2,2,2,2]
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> ? = 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> ? = 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [4,4,4,4,4]
=> ? = 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [2,2]
=> 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ? = 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [2,2]
=> 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> ? = 3
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> ? = 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ? = 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [2,2,2,2,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ? = 5
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [6,6,6]
=> ? = 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ? = 3
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ? = 2
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ? = 3
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [3,3,3,3,1,1,1,1,1,1]
=> ? = 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [2,2]
=> 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [2,2,2,2,2,2,2,2]
=> ? = 2
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [2,2,2,2,2,2,2,2,2,2]
=> ? = 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,4,4,4,4,4,4,4,4,4,4]
=> ?
=> ? = 4
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [2,2]
=> 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [3,3,2,2,1,1,1,1]
=> ? = 3
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [2,2]
=> 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [2,2]
=> 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
=> [2,2]
=> [2,2]
=> 1
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
=> [6]
=> [1,1,1,1,1,1]
=> 1
Description
The number of monotone factorisations of genus zero of a permutation of given cycle type. A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions $$ (a_1, b_1),\dots,(a_r, b_r) $$ with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$. For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.
Mp00307: Posets promotion cycle typeInteger partitions
Mp00179: Integer partitions to skew partitionSkew partitions
St001658: Skew partitions ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 11%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [[15,15],[]]
=> ? = 1 + 6
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [[15,15],[]]
=> ? = 1 + 6
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [[10,10],[]]
=> ? = 3 + 6
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [[12,4],[]]
=> ? = 2 + 6
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [[14],[]]
=> ? = 1 + 6
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [[6,6],[]]
=> ? = 1 + 6
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [[10,4,4],[]]
=> ? = 1 + 6
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [[15,5,5],[]]
=> ? = 2 + 6
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [[5,4],[]]
=> ? = 1 + 6
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [[5,5,5,5],[]]
=> ? = 1 + 6
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [[10,10],[]]
=> ? = 3 + 6
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [[10,4,4],[]]
=> ? = 1 + 6
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [[12,4],[]]
=> ? = 2 + 6
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [[14],[]]
=> ? = 1 + 6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [[6,6],[]]
=> ? = 1 + 6
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [[5,3],[]]
=> ? = 1 + 6
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [[5,4],[]]
=> ? = 1 + 6
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [[5,5],[]]
=> ? = 2 + 6
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [[15,15],[]]
=> ? = 1 + 6
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [[10,10],[]]
=> ? = 3 + 6
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [[12,4],[]]
=> ? = 2 + 6
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [[14],[]]
=> ? = 1 + 6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [[6,6],[]]
=> ? = 1 + 6
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [[10,4,4],[]]
=> ? = 1 + 6
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [[15,5,5],[]]
=> ? = 2 + 6
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [[5,5,5,5],[]]
=> ? = 1 + 6
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [[15,15],[]]
=> ? = 1 + 6
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ? = 2 + 6
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [[10,10],[]]
=> ? = 3 + 6
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [[10,4,4],[]]
=> ? = 1 + 6
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [[12,4],[]]
=> ? = 2 + 6
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [[14],[]]
=> ? = 1 + 6
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [[6,6],[]]
=> ? = 1 + 6
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ? = 2 + 6
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [[6,6],[]]
=> ? = 1 + 6
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [[6,6],[]]
=> ? = 1 + 6
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [[15,15],[]]
=> ? = 1 + 6
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [[12,4],[]]
=> ? = 2 + 6
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ? = 5 + 6
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [[14],[]]
=> ? = 1 + 6
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [[3,3,3,3,3,3],[]]
=> ? = 3 + 6
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [[6,6],[]]
=> ? = 1 + 6
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ? = 3 + 6
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ? = 2 + 6
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ? = 3 + 6
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [[10,4,4],[]]
=> ? = 1 + 6
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [[8,8],[]]
=> ? = 2 + 6
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [[10,10],[]]
=> ? = 3 + 6
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,4,4,4,4,4,4,4,4,4,4]
=> ?
=> ? = 4 + 6
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [[8,4,2],[]]
=> ? = 3 + 6
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
=> [2,2]
=> [[2,2],[]]
=> 7 = 1 + 6
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
=> [6]
=> [[6],[]]
=> 7 = 1 + 6
Description
The total number of rook placements on a Ferrers board.
Mp00307: Posets promotion cycle typeInteger partitions
Mp00042: Integer partitions initial tableauStandard tableaux
Mp00084: Standard tableaux conjugateStandard tableaux
St001816: Standard tableaux ⟶ ℤResult quality: 8% values known / values provided: 8%distinct values known / distinct values provided: 11%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 1 - 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14]]
=> ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> ? = 1 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25]]
=> [[1,16,21],[2,17,22],[3,18,23],[4,19,24],[5,20,25],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]]
=> ? = 2 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [[1,2,3,4,5],[6,7,8,9]]
=> [[1,6],[2,7],[3,8],[4,9],[5]]
=> ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 3 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14]]
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> ? = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [[1,6],[2,7],[3,8],[4],[5]]
=> ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [[1,2,3,4,5],[6,7,8,9]]
=> [[1,6],[2,7],[3,8],[4,9],[5]]
=> ? = 1 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 3 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14]]
=> ? = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25]]
=> [[1,16,21],[2,17,22],[3,18,23],[4,19,24],[5,20,25],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]]
=> ? = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]
=> [[1,6,11,16],[2,7,12,17],[3,8,13,18],[4,9,14,19],[5,10,15,20]]
=> ? = 1 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 1 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 3 - 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 1 - 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14]]
=> ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> ? = 1 - 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]]
=> [[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,25],[11,26],[12,27],[13,28],[14,29],[15,30]]
=> ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [[1,2,3,4,5,6,7,8,9,10,11,12],[13,14,15,16]]
=> [[1,13],[2,14],[3,15],[4,16],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 5 - 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14]]
=> ? = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18]]
=> [[1,4,7,10,13,16],[2,5,8,11,14,17],[3,6,9,12,15,18]]
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [[1,2,3,4,5,6],[7,8,9,10,11,12]]
=> [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
=> ? = 1 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ?
=> ? = 3 - 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ?
=> ? = 2 - 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14],[15,16,17,18]]
=> [[1,11,15],[2,12,16],[3,13,17],[4,14,18],[5],[6],[7],[8],[9],[10]]
=> ? = 1 - 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [8,8]
=> [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]]
=> [[1,9],[2,10],[3,11],[4,12],[5,13],[6,14],[7,15],[8,16]]
=> ? = 2 - 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [10,10]
=> [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]
=> [[1,11],[2,12],[3,13],[4,14],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20]]
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,4,4,4,4,4,4,4,4,4,4,4]
=> ?
=> ?
=> ? = 4 - 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> [8,4,2]
=> [[1,2,3,4,5,6,7,8],[9,10,11,12],[13,14]]
=> ?
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
=> [2,2]
=> [[1,2],[3,4]]
=> [[1,3],[2,4]]
=> 0 = 1 - 1
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 0 = 1 - 1
Description
Eigenvalues of the top-to-random operator acting on a simple module. These eigenvalues are given in [1] and [3]. The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module. This statistic bears different names, such as the type in [2] or eig in [3]. Similarly, the eigenvalues of the random-to-random operator acting on a simple module is [[St000508]].
Mp00307: Posets promotion cycle typeInteger partitions
Mp00230: Integer partitions parallelogram polyominoDyck paths
Mp00227: Dyck paths Delest-Viennot-inverseDyck paths
St001514: Dyck paths ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 33%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0]
=> ? = 2
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [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
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0]
=> ? = 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [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
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 5
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> ? = 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ?
=> ? = 3
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [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
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ?
=> ? = 2
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 3
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 2
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 2
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 1
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 2
Description
The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule.
Mp00307: Posets promotion cycle typeInteger partitions
Mp00230: Integer partitions parallelogram polyominoDyck paths
Mp00227: Dyck paths Delest-Viennot-inverseDyck paths
St001200: Dyck paths ⟶ ℤResult quality: 7% values known / values provided: 7%distinct values known / distinct values provided: 33%
Values
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,4),(2,3),(2,4)],5)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(1,2),(1,3)],5)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [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 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [15,5,5]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,5,5,5]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
=> ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [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 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [10,10]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 3 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [12,12]
=> ?
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [15,15]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [12,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
=> ? = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 5 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [14]
=> [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]
=> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,3,3,3,3,3]
=> [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [8,3,3,3,3]
=> ?
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [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 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [8,5,5]
=> ?
=> ?
=> ? = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [18,3,3]
=> ?
=> ?
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [10,4,4]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
=> [2,2,2,2]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 3 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
=> [4,4]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 2 = 1 + 1
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2 = 1 + 1
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 3 = 2 + 1
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
The following 35 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001625The Möbius invariant of a lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001488The number of corners of a skew partition. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001621The number of atoms of a lattice. St001623The number of doubly irreducible elements of a lattice. St001624The breadth of a lattice. St001626The number of maximal proper sublattices of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001875The number of simple modules with projective dimension at most 1. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001754The number of tolerances of a finite lattice. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000950Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path.