searching the database
Your data matches 25 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001879
Values
([(0,2),(2,1)],3)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(0,3),(2,1),(3,2)],4)
=> 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> 10
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 8
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> 10
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 8
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> 17
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> 17
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> 18
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 11
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> 11
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> 11
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> 15
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> 17
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> 10
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> 11
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> 12
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> 9
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> 16
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 8
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> 12
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> 17
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> 20
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> 13
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> 13
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> 14
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> 12
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> 15
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> 13
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> 13
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> 11
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St000738
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000738: Standard tableaux ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 37%
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000738: Standard tableaux ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 37%
Values
([(0,2),(2,1)],3)
=> [4]
=> [[1,2,3,4]]
=> [[1],[2],[3],[4]]
=> 4 = 2 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> [4,2]
=> [[1,2,5,6],[3,4]]
=> [[1,3],[2,4],[5],[6]]
=> 6 = 4 + 2
([(0,3),(2,1),(3,2)],4)
=> [5]
=> [[1,2,3,4,5]]
=> [[1],[2],[3],[4],[5]]
=> 5 = 3 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [4,2,2,2]
=> [[1,2,9,10],[3,4],[5,6],[7,8]]
=> [[1,3,5,7],[2,4,6,8],[9],[10]]
=> ? = 9 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [5,2]
=> [[1,2,5,6,7],[3,4]]
=> [[1,3],[2,4],[5],[6],[7]]
=> 7 = 5 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [8]
=> [[1,2,3,4,5,6,7,8]]
=> [[1],[2],[3],[4],[5],[6],[7],[8]]
=> 8 = 6 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> [6]
=> [[1,2,3,4,5,6]]
=> [[1],[2],[3],[4],[5],[6]]
=> 6 = 4 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> [5,2]
=> [[1,2,5,6,7],[3,4]]
=> [[1,3],[2,4],[5],[6],[7]]
=> 7 = 5 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,2,2,2,2,2,2,2]
=> ?
=> ?
=> ? = 16 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [5,2,2,2]
=> [[1,2,9,10,11],[3,4],[5,6],[7,8]]
=> [[1,3,5,7],[2,4,6,8],[9],[10],[11]]
=> ? = 10 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8,2,2]
=> [[1,2,7,8,9,10,11,12],[3,4],[5,6]]
=> ?
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [5,3,3]
=> [[1,2,3,10,11],[4,5,6],[7,8,9]]
=> [[1,4,7],[2,5,8],[3,6,9],[10],[11]]
=> ? = 8 + 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8,2,2]
=> [[1,2,7,8,9,10,11,12],[3,4],[5,6]]
=> ?
=> ? = 10 + 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [5,2,2,2]
=> [[1,2,9,10,11],[3,4],[5,6],[7,8]]
=> [[1,3,5,7],[2,4,6,8],[9],[10],[11]]
=> ? = 10 + 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [8,6]
=> [[1,2,3,4,5,6,13,14],[7,8,9,10,11,12]]
=> ?
=> ? = 12 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> [5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10]]
=> ? = 7 + 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> [9]
=> [[1,2,3,4,5,6,7,8,9]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
=> 9 = 7 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> [6,4]
=> [[1,2,3,4,9,10],[5,6,7,8]]
=> [[1,5],[2,6],[3,7],[4,8],[9],[10]]
=> ? = 8 + 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> [6,2]
=> [[1,2,5,6,7,8],[3,4]]
=> [[1,3],[2,4],[5],[6],[7],[8]]
=> 8 = 6 + 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> [6,2]
=> [[1,2,5,6,7,8],[3,4]]
=> [[1,3],[2,4],[5],[6],[7],[8]]
=> 8 = 6 + 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> [7]
=> [[1,2,3,4,5,6,7]]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> 7 = 5 + 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> [6,2]
=> [[1,2,5,6,7,8],[3,4]]
=> [[1,3],[2,4],[5],[6],[7],[8]]
=> 8 = 6 + 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> [9]
=> [[1,2,3,4,5,6,7,8,9]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9]]
=> 9 = 7 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ?
=> ?
=> ? = 25 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> [5,2,2,2,2,2,2,2]
=> ?
=> ?
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> [8,2,2,2,2,2,2]
=> [[1,2,15,16,17,18,19,20],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]]
=> ?
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [8,6,2,2,2,2]
=> ?
=> ?
=> ? = 18 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> [8,5,2]
=> [[1,2,5,6,7,13,14,15],[3,4,10,11,12],[8,9]]
=> ?
=> ? = 11 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> [9,2,2]
=> [[1,2,7,8,9,10,11,12,13],[3,4],[5,6]]
=> ?
=> ? = 11 + 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> [6,2,2,2]
=> [[1,2,9,10,11,12],[3,4],[5,6],[7,8]]
=> ?
=> ? = 11 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> [8,6,6]
=> ?
=> ?
=> ? = 15 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> [8,6,2,2,2,2]
=> ?
=> ?
=> ? = 17 + 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> [8,5,2]
=> [[1,2,5,6,7,13,14,15],[3,4,10,11,12],[8,9]]
=> ?
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> [6,4,2,2]
=> [[1,2,7,8,13,14],[3,4,11,12],[5,6],[9,10]]
=> ?
=> ? = 11 + 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> [6,5,5]
=> [[1,2,3,4,5,16],[6,7,8,9,10],[11,12,13,14,15]]
=> ?
=> ? = 12 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> [12]
=> [[1,2,3,4,5,6,7,8,9,10,11,12]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> [8,2,2,2,2,2,2]
=> [[1,2,15,16,17,18,19,20],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]]
=> ?
=> ? = 16 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [6,2,2]
=> [[1,2,7,8,9,10],[3,4],[5,6]]
=> [[1,3,5],[2,4,6],[7],[8],[9],[10]]
=> ? = 8 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> [6,5,3,3]
=> [[1,2,3,10,11,17],[4,5,6,15,16],[7,8,9],[12,13,14]]
=> ?
=> ? = 12 + 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> [5,2,2,2,2,2,2,2]
=> ?
=> ?
=> ? = 17 + 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> [7,2]
=> [[1,2,5,6,7,8,9],[3,4]]
=> [[1,3],[2,4],[5],[6],[7],[8],[9]]
=> ? = 7 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> [8,6,6,6]
=> ?
=> ?
=> ? = 20 + 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> [9,6]
=> [[1,2,3,4,5,6,13,14,15],[7,8,9,10,11,12]]
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> [16]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> [10,8]
=> ?
=> ?
=> ? = 14 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> [6,4,2,2]
=> [[1,2,7,8,13,14],[3,4,11,12],[5,6],[9,10]]
=> ?
=> ? = 12 + 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> [6,4,4,4]
=> ?
=> ?
=> ? = 15 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> [6,5,5]
=> [[1,2,3,4,5,16],[6,7,8,9,10],[11,12,13,14,15]]
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> [6,5,3,3]
=> [[1,2,3,10,11,17],[4,5,6,15,16],[7,8,9],[12,13,14]]
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> [6,2,2,2]
=> [[1,2,9,10,11,12],[3,4],[5,6],[7,8]]
=> ?
=> ? = 11 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> [6,5]
=> [[1,2,3,4,5,11],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10],[11]]
=> ? = 8 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> [7,4]
=> [[1,2,3,4,9,10,11],[5,6,7,8]]
=> ?
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> [9,2,2]
=> [[1,2,7,8,9,10,11,12,13],[3,4],[5,6]]
=> ?
=> ? = 11 + 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> [7,2]
=> [[1,2,5,6,7,8,9],[3,4]]
=> [[1,3],[2,4],[5],[6],[7],[8],[9]]
=> ? = 7 + 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> [6,3,3]
=> [[1,2,3,10,11,12],[4,5,6],[7,8,9]]
=> ?
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> [12]
=> [[1,2,3,4,5,6,7,8,9,10,11,12]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> [10,3]
=> [[1,2,3,7,8,9,10,11,12,13],[4,5,6]]
=> ?
=> ? = 9 + 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> [6,5]
=> [[1,2,3,4,5,11],[6,7,8,9,10]]
=> [[1,6],[2,7],[3,8],[4,9],[5,10],[11]]
=> ? = 8 + 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> [6,2,2,2]
=> [[1,2,9,10,11,12],[3,4],[5,6],[7,8]]
=> ?
=> ? = 11 + 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> [10]
=> [[1,2,3,4,5,6,7,8,9,10]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
=> 10 = 8 + 2
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
=> [10,3]
=> [[1,2,3,7,8,9,10,11,12,13],[4,5,6]]
=> ?
=> ? = 9 + 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> [12]
=> [[1,2,3,4,5,6,7,8,9,10,11,12]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
=> ? = 10 + 2
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
=> [16]
=> [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]
=> ?
=> ? = 13 + 2
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
=> [6,4,2,2]
=> [[1,2,7,8,13,14],[3,4,11,12],[5,6],[9,10]]
=> ?
=> ? = 12 + 2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> [10]
=> [[1,2,3,4,5,6,7,8,9,10]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
=> 10 = 8 + 2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> [8]
=> [[1,2,3,4,5,6,7,8]]
=> [[1],[2],[3],[4],[5],[6],[7],[8]]
=> 8 = 6 + 2
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> [10]
=> [[1,2,3,4,5,6,7,8,9,10]]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
=> 10 = 8 + 2
Description
The first entry in the last row of a standard tableau.
For the last entry in the first row, see [[St000734]].
Matching statistic: St001846
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 4
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ? = 9
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 5
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> 6
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 5
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ? = 16
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ? = 10
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ? = 10
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ? = 8
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 10
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ? = 10
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ? = 12
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 7
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> 7
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ? = 8
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> 6
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> 6
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 5
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> 6
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> 7
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 25
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ? = 17
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ? = 17
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ?
=> ? = 18
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ? = 11
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ? = 11
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 11
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ? = 15
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ?
=> ? = 17
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ? = 10
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ? = 11
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ? = 12
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ? = 9
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ? = 16
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ? = 8
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ? = 12
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ? = 17
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> 7
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ?
=> ? = 20
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ? = 13
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ? = 13
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ? = 14
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ? = 12
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ? = 15
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ? = 13
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ? = 13
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ? = 11
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ? = 8
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ? = 9
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ? = 11
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> 7
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ? = 9
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ? = 9
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ? = 9
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11)
=> ? = 8
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,7),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,5)],12)
=> ? = 11
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ([(0,6),(2,9),(3,8),(4,2),(4,8),(5,1),(6,7),(7,3),(7,4),(8,9),(9,5)],10)
=> ? = 8
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,12),(3,11),(4,10),(5,3),(5,8),(6,4),(6,8),(7,5),(7,6),(8,10),(8,11),(9,12),(10,9),(11,2),(11,9),(12,1)],13)
=> ? = 9
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,7),(2,8),(3,11),(4,5),(4,8),(5,6),(5,10),(6,3),(6,9),(7,2),(7,4),(8,10),(9,11),(10,9),(11,1)],12)
=> ? = 10
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
=> ([(0,7),(1,9),(3,8),(3,12),(4,10),(4,11),(5,4),(5,8),(5,13),(6,3),(6,5),(6,9),(7,1),(7,6),(8,11),(8,14),(9,12),(9,13),(10,15),(11,15),(12,14),(13,10),(13,14),(14,15),(15,2)],16)
=> ? = 13
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
=> ([(0,7),(1,9),(3,8),(3,11),(4,8),(4,10),(5,6),(5,9),(6,3),(6,4),(6,12),(7,1),(7,5),(8,13),(9,12),(10,13),(11,13),(12,10),(12,11),(13,2)],14)
=> ? = 12
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> ([(0,7),(1,9),(3,8),(4,2),(5,1),(5,8),(6,4),(7,3),(7,5),(8,9),(9,6)],10)
=> ? = 8
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> 6
Description
The number of elements which do not have a complement in the lattice.
A complement of an element $x$ in a lattice is an element $y$ such that the meet of $x$ and $y$ is the bottom element and their join is the top element.
Matching statistic: St001616
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 2 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ? = 9 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7 = 5 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> 8 = 6 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7 = 5 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ? = 16 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ? = 10 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ? = 8 + 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 10 + 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ? = 10 + 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ? = 12 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 7 + 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> 9 = 7 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ? = 8 + 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> 8 = 6 + 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> 8 = 6 + 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> 8 = 6 + 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> 9 = 7 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 25 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ?
=> ? = 18 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ? = 11 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ? = 11 + 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 11 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ? = 15 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ?
=> ? = 17 + 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ? = 11 + 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ? = 12 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ? = 16 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ? = 8 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ? = 12 + 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ? = 17 + 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> 9 = 7 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ?
=> ? = 20 + 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ? = 14 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ? = 12 + 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ? = 15 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ? = 11 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ? = 8 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ? = 11 + 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> 9 = 7 + 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ? = 9 + 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11)
=> ? = 8 + 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,7),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,5)],12)
=> ? = 11 + 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ([(0,6),(2,9),(3,8),(4,2),(4,8),(5,1),(6,7),(7,3),(7,4),(8,9),(9,5)],10)
=> ? = 8 + 2
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,12),(3,11),(4,10),(5,3),(5,8),(6,4),(6,8),(7,5),(7,6),(8,10),(8,11),(9,12),(10,9),(11,2),(11,9),(12,1)],13)
=> ? = 9 + 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,7),(2,8),(3,11),(4,5),(4,8),(5,6),(5,10),(6,3),(6,9),(7,2),(7,4),(8,10),(9,11),(10,9),(11,1)],12)
=> ? = 10 + 2
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
=> ([(0,7),(1,9),(3,8),(3,12),(4,10),(4,11),(5,4),(5,8),(5,13),(6,3),(6,5),(6,9),(7,1),(7,6),(8,11),(8,14),(9,12),(9,13),(10,15),(11,15),(12,14),(13,10),(13,14),(14,15),(15,2)],16)
=> ? = 13 + 2
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
=> ([(0,7),(1,9),(3,8),(3,11),(4,8),(4,10),(5,6),(5,9),(6,3),(6,4),(6,12),(7,1),(7,5),(8,13),(9,12),(10,13),(11,13),(12,10),(12,11),(13,2)],14)
=> ? = 12 + 2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> ([(0,7),(1,9),(3,8),(4,2),(5,1),(5,8),(6,4),(7,3),(7,5),(8,9),(9,6)],10)
=> ? = 8 + 2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> 8 = 6 + 2
Description
The number of neutral elements in a lattice.
An element $e$ of the lattice $L$ is neutral if the sublattice generated by $e$, $x$ and $y$ is distributive for all $x, y \in L$.
Matching statistic: St000479
Values
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4 = 2 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(4,5)],6)
=> 6 = 4 + 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5 = 3 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
=> ? = 9 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(5,6)],7)
=> 7 = 5 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> 8 = 6 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6 = 4 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(5,6)],7)
=> 7 = 5 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ?
=> ? = 16 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ?
=> ? = 10 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ?
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ?
=> ? = 8 + 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ?
=> ? = 10 + 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ?
=> ? = 10 + 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ?
=> ? = 12 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ([(4,9),(5,8),(6,7),(7,9),(8,9)],10)
=> ? = 7 + 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ?
=> ? = 7 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ?
=> ? = 8 + 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ?
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ([(6,7)],8)
=> 8 = 6 + 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 7 = 5 + 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ?
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ?
=> ? = 7 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ?
=> ?
=> ? = 25 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ?
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ?
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ?
=> ?
=> ?
=> ? = 18 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ?
=> ? = 11 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ?
=> ? = 11 + 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ?
=> ? = 11 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ?
=> ? = 15 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ?
=> ?
=> ?
=> ? = 17 + 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ?
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ?
=> ? = 11 + 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ?
=> ? = 12 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ?
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ?
=> ? = 16 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ?
=> ? = 8 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ?
=> ? = 12 + 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ?
=> ? = 17 + 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ?
=> ? = 7 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ?
=> ?
=> ?
=> ? = 20 + 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ?
=> ? = 14 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ?
=> ? = 12 + 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ?
=> ? = 15 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ?
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ?
=> ? = 11 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ([(5,10),(6,9),(7,8),(8,10),(9,10)],11)
=> ? = 8 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ?
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ?
=> ? = 11 + 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ?
=> ? = 7 + 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ?
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ?
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ?
=> ? = 9 + 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11)
=> ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11)
=> ([(5,10),(6,9),(7,8),(8,10),(9,10)],11)
=> ? = 8 + 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,7),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,5)],12)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,7),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,5)],12)
=> ?
=> ? = 11 + 2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> ([],8)
=> 8 = 6 + 2
Description
The Ramsey number of a graph.
This is the smallest integer $n$ such that every two-colouring of the edges of the complete graph $K_n$ contains a (not necessarily induced) monochromatic copy of the given graph. [1]
Thus, the Ramsey number of the complete graph $K_n$ is the ordinary Ramsey number $R(n,n)$. Very few of these numbers are known, in particular, it is only known that $43\leq R(5,5)\leq 48$. [2,3,4,5]
Matching statistic: St000550
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 2 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ? = 9 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7 = 5 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 6 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7 = 5 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ? = 16 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ? = 10 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ? = 8 + 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 10 + 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ? = 10 + 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ? = 12 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 7 + 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ? = 7 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ? = 8 + 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 6 + 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ? = 7 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 25 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ?
=> ? = 18 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ? = 11 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ? = 11 + 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 11 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ? = 15 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ?
=> ? = 17 + 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ? = 11 + 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ? = 12 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ? = 16 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ? = 8 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ? = 12 + 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ? = 17 + 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ? = 7 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ?
=> ? = 20 + 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ? = 14 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ? = 12 + 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ? = 15 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ? = 11 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ? = 8 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ? = 11 + 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ? = 7 + 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ? = 9 + 2
Description
The number of modular elements of a lattice.
A pair $(x, y)$ of elements of a lattice $L$ is a modular pair if for every $z\geq y$ we have that $(y\vee x) \wedge z = y \vee (x \wedge z)$. An element $x$ is left-modular if $(x, y)$ is a modular pair for every $y\in L$, and is modular if both $(x, y)$ and $(y, x)$ are modular pairs for every $y\in L$.
Matching statistic: St000551
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 2 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ? = 9 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7 = 5 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 6 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7 = 5 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ? = 16 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ? = 10 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ? = 8 + 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 10 + 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ? = 10 + 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ? = 12 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 7 + 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ? = 7 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ? = 8 + 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 6 + 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ? = 7 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ? = 25 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ?
=> ? = 18 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ? = 11 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ? = 11 + 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 11 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ? = 15 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ?
=> ? = 17 + 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ? = 11 + 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ? = 12 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ? = 16 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ? = 8 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ? = 12 + 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ? = 17 + 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ? = 7 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ?
=> ? = 20 + 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ? = 14 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ? = 12 + 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ? = 15 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ? = 11 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ? = 8 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ? = 11 + 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ? = 7 + 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ? = 9 + 2
Description
The number of left modular elements of a lattice.
A pair $(x, y)$ of elements of a lattice $L$ is a modular pair if for every $z\geq y$ we have that $(y\vee x) \wedge z = y \vee (x \wedge z)$. An element $x$ is left-modular if $(x, y)$ is a modular pair for every $y\in L$.
Matching statistic: St001614
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001614: Skew partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 21%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001614: Skew partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 21%
Values
([(0,2),(2,1)],3)
=> [4]
=> [[4],[]]
=> 4 = 2 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> [4,2]
=> [[4,2],[]]
=> 6 = 4 + 2
([(0,3),(2,1),(3,2)],4)
=> [5]
=> [[5],[]]
=> 5 = 3 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [4,2,2,2]
=> [[4,2,2,2],[]]
=> ? = 9 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [5,2]
=> [[5,2],[]]
=> 7 = 5 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [8]
=> [[8],[]]
=> ? = 6 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> [6]
=> [[6],[]]
=> 6 = 4 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> [5,2]
=> [[5,2],[]]
=> 7 = 5 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,2,2,2,2,2,2,2]
=> ?
=> ? = 16 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [5,2,2,2]
=> [[5,2,2,2],[]]
=> ? = 10 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8,2,2]
=> [[8,2,2],[]]
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [5,3,3]
=> [[5,3,3],[]]
=> ? = 8 + 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8,2,2]
=> [[8,2,2],[]]
=> ? = 10 + 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [5,2,2,2]
=> [[5,2,2,2],[]]
=> ? = 10 + 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [8,6]
=> [[8,6],[]]
=> ? = 12 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> [5,5]
=> [[5,5],[]]
=> ? = 7 + 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> [9]
=> [[9],[]]
=> ? = 7 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> [6,4]
=> [[6,4],[]]
=> ? = 8 + 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> [6,2]
=> [[6,2],[]]
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> [6,2]
=> [[6,2],[]]
=> ? = 6 + 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> [7]
=> [[7],[]]
=> 7 = 5 + 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> [6,2]
=> [[6,2],[]]
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> [9]
=> [[9],[]]
=> ? = 7 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ?
=> ? = 25 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> [5,2,2,2,2,2,2,2]
=> ?
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> [8,2,2,2,2,2,2]
=> [[8,2,2,2,2,2,2],[]]
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [8,6,2,2,2,2]
=> ?
=> ? = 18 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> [8,5,2]
=> [[8,5,2],[]]
=> ? = 11 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> [9,2,2]
=> [[9,2,2],[]]
=> ? = 11 + 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> [6,2,2,2]
=> [[6,2,2,2],[]]
=> ? = 11 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> [8,6,6]
=> ?
=> ? = 15 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> [8,6,2,2,2,2]
=> ?
=> ? = 17 + 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> [8,5,2]
=> [[8,5,2],[]]
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> [6,4,2,2]
=> [[6,4,2,2],[]]
=> ? = 11 + 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> [6,5,5]
=> [[6,5,5],[]]
=> ? = 12 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> [12]
=> [[12],[]]
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> [8,2,2,2,2,2,2]
=> [[8,2,2,2,2,2,2],[]]
=> ? = 16 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> [6,2,2]
=> [[6,2,2],[]]
=> ? = 8 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> [6,5,3,3]
=> [[6,5,3,3],[]]
=> ? = 12 + 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> [5,2,2,2,2,2,2,2]
=> ?
=> ? = 17 + 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> [7,2]
=> [[7,2],[]]
=> ? = 7 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> [8,6,6,6]
=> ?
=> ? = 20 + 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> [9,6]
=> [[9,6],[]]
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> [16]
=> [[16],[]]
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> [10,8]
=> ?
=> ? = 14 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> [6,4,2,2]
=> [[6,4,2,2],[]]
=> ? = 12 + 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> [6,4,4,4]
=> ?
=> ? = 15 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> [6,5,5]
=> [[6,5,5],[]]
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> [6,5,3,3]
=> [[6,5,3,3],[]]
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> [6,2,2,2]
=> [[6,2,2,2],[]]
=> ? = 11 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> [6,5]
=> [[6,5],[]]
=> ? = 8 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> [7,4]
=> [[7,4],[]]
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> [9,2,2]
=> [[9,2,2],[]]
=> ? = 11 + 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> [7,2]
=> [[7,2],[]]
=> ? = 7 + 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> [6,3,3]
=> [[6,3,3],[]]
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> [12]
=> [[12],[]]
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> [10,3]
=> [[10,3],[]]
=> ? = 9 + 2
Description
The cyclic permutation representation number of a skew partition.
This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$.
See [[St001527]] for the restriction of this statistic to integer partitions.
Matching statistic: St001880
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 2 + 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ? = 9 + 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7 = 5 + 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 6 + 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7 = 5 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ? = 16 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ? = 10 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ? = 8 + 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 10 + 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ? = 10 + 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ? = 12 + 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 7 + 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ? = 7 + 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ? = 8 + 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 6 + 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ? = 6 + 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ? = 7 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 25 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ? = 17 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ?
=> ?
=> ? = 18 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ? = 11 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ? = 11 + 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ? = 11 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ? = 15 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ?
=> ?
=> ? = 17 + 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ? = 10 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ? = 11 + 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ? = 12 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ? = 16 + 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ? = 8 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ? = 12 + 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ? = 17 + 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ? = 7 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ?
=> ?
=> ? = 20 + 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ? = 14 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ? = 12 + 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ? = 15 + 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ? = 13 + 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ? = 11 + 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ? = 8 + 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ? = 9 + 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ? = 11 + 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ? = 7 + 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ? = 9 + 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ? = 9 + 2
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000987
Values
([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 3 = 2 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> 5 = 4 + 1
([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4 = 3 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ([(0,9),(1,8),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,9),(6,9),(7,9)],10)
=> ? = 9 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
=> 6 = 5 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
=> ? = 6 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 5 = 4 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
=> 6 = 5 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
=> ?
=> ? = 16 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
=> ?
=> ? = 10 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
=> ?
=> ? = 10 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ?
=> ? = 8 + 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ([(0,6),(2,7),(3,8),(3,10),(4,8),(4,9),(5,3),(5,4),(5,7),(6,2),(6,5),(7,9),(7,10),(8,11),(9,11),(10,11),(11,1)],12)
=> ?
=> ? = 10 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ([(0,5),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,6),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,1)],11)
=> ?
=> ? = 10 + 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ([(0,6),(2,10),(2,11),(3,7),(3,9),(4,7),(4,8),(5,2),(5,8),(5,9),(6,3),(6,4),(6,5),(7,12),(8,10),(8,12),(9,11),(9,12),(10,13),(11,13),(12,13),(13,1)],14)
=> ?
=> ? = 12 + 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10)
=> ? = 7 + 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> ?
=> ? = 7 + 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ?
=> ? = 8 + 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> ?
=> ? = 6 + 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
=> ? = 6 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
=> 6 = 5 + 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> ?
=> ? = 6 + 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> ?
=> ? = 7 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ?
=> ?
=> ?
=> ? = 25 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ([(0,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,1),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,6)],19)
=> ?
=> ? = 17 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ([(0,7),(1,14),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,11),(6,12),(6,13),(7,3),(7,4),(7,5),(7,6),(8,17),(8,18),(9,15),(9,18),(10,16),(10,18),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,2),(15,19),(16,19),(17,19),(18,1),(18,19),(19,14)],20)
=> ?
=> ? = 17 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ?
=> ?
=> ?
=> ? = 18 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ([(0,7),(2,11),(2,12),(3,10),(4,9),(5,8),(5,11),(6,8),(6,12),(7,2),(7,5),(7,6),(8,14),(9,13),(10,13),(11,4),(11,14),(12,3),(12,14),(13,1),(14,9),(14,10)],15)
=> ?
=> ? = 11 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ([(0,7),(2,10),(3,9),(3,11),(4,8),(4,11),(5,8),(5,9),(6,1),(7,3),(7,4),(7,5),(8,12),(9,12),(10,6),(11,2),(11,12),(12,10)],13)
=> ?
=> ? = 11 + 1
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ([(0,6),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,7),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,1)],12)
=> ?
=> ? = 11 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ([(0,2),(2,3),(2,4),(2,5),(3,13),(3,14),(4,7),(4,14),(4,15),(5,6),(5,13),(5,15),(6,9),(6,11),(7,10),(7,12),(8,19),(9,17),(10,18),(11,8),(11,17),(12,8),(12,18),(13,9),(13,16),(14,10),(14,16),(15,11),(15,12),(15,16),(16,17),(16,18),(17,19),(18,19),(19,1)],20)
=> ?
=> ? = 15 + 1
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ?
=> ?
=> ?
=> ? = 17 + 1
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ([(0,7),(1,10),(1,11),(3,9),(4,8),(5,4),(5,13),(6,3),(6,13),(7,5),(7,6),(8,10),(8,12),(9,11),(9,12),(10,14),(11,14),(12,14),(13,1),(13,8),(13,9),(14,2)],15)
=> ?
=> ? = 10 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ([(0,7),(2,8),(3,12),(4,10),(4,11),(5,9),(5,11),(6,4),(6,5),(6,8),(7,2),(7,6),(8,9),(8,10),(9,13),(10,13),(11,3),(11,13),(12,1),(13,12)],14)
=> ?
=> ? = 11 + 1
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ([(0,7),(2,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,4),(6,5),(6,13),(7,2),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,15),(12,15),(13,3),(13,9),(13,10),(14,15),(15,1)],16)
=> ?
=> ? = 12 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ([(0,7),(1,11),(3,8),(4,10),(5,4),(5,8),(6,1),(6,9),(7,3),(7,5),(8,6),(8,10),(9,11),(10,9),(11,2)],12)
=> ?
=> ? = 9 + 1
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ([(0,6),(2,8),(3,10),(3,11),(3,14),(4,9),(4,11),(4,13),(5,9),(5,10),(5,12),(6,2),(6,7),(7,3),(7,4),(7,5),(7,8),(8,12),(8,13),(8,14),(9,17),(9,18),(10,15),(10,18),(11,16),(11,18),(12,15),(12,17),(13,16),(13,17),(14,15),(14,16),(15,19),(16,19),(17,19),(18,19),(19,1)],20)
=> ?
=> ? = 16 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ([(0,7),(2,9),(3,9),(4,8),(5,8),(6,2),(6,3),(7,4),(7,5),(8,6),(9,1)],10)
=> ?
=> ? = 8 + 1
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ([(0,7),(2,8),(2,12),(3,8),(3,11),(4,10),(5,4),(5,9),(6,2),(6,3),(6,9),(7,5),(7,6),(8,15),(9,10),(9,11),(9,12),(10,13),(10,14),(11,13),(11,15),(12,14),(12,15),(13,16),(14,16),(15,16),(16,1)],17)
=> ?
=> ? = 12 + 1
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ([(0,6),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,7),(7,2),(7,3),(7,4),(7,5),(8,14),(8,17),(9,14),(9,15),(10,14),(10,16),(11,15),(11,17),(12,16),(12,17),(13,15),(13,16),(14,18),(15,18),(16,18),(17,18),(18,1)],19)
=> ?
=> ? = 17 + 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> ?
=> ? = 7 + 1
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ?
=> ?
=> ?
=> ? = 20 + 1
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ([(0,7),(1,11),(1,12),(3,8),(3,10),(4,8),(4,9),(5,2),(6,1),(6,9),(6,10),(7,3),(7,4),(7,6),(8,14),(9,11),(9,14),(10,12),(10,14),(11,13),(12,13),(13,5),(14,13)],15)
=> ?
=> ? = 13 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ([(0,7),(1,12),(3,11),(3,13),(4,8),(4,9),(5,8),(5,10),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,13),(9,15),(10,11),(10,15),(11,14),(12,2),(13,1),(13,14),(14,12),(15,14)],16)
=> ?
=> ? = 13 + 1
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ([(0,7),(2,9),(2,12),(3,8),(3,14),(4,11),(4,13),(5,8),(5,10),(6,4),(6,10),(6,14),(7,3),(7,5),(7,6),(8,16),(9,17),(10,13),(10,16),(11,12),(11,15),(12,17),(13,15),(14,2),(14,11),(14,16),(15,17),(16,9),(16,15),(17,1)],18)
=> ?
=> ? = 14 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ([(0,7),(2,12),(3,8),(3,9),(4,9),(4,10),(5,8),(5,10),(6,2),(6,11),(7,3),(7,4),(7,5),(8,13),(9,13),(10,6),(10,13),(11,12),(12,1),(13,11)],14)
=> ?
=> ? = 12 + 1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ([(0,7),(2,8),(2,10),(3,8),(3,9),(4,11),(4,12),(5,6),(5,9),(5,10),(6,4),(6,13),(6,14),(7,2),(7,3),(7,5),(8,15),(9,13),(9,15),(10,14),(10,15),(11,17),(12,17),(13,11),(13,16),(14,12),(14,16),(15,16),(16,17),(17,1)],18)
=> ?
=> ? = 15 + 1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ([(0,7),(1,13),(3,11),(3,12),(4,8),(4,10),(5,8),(5,9),(6,3),(6,9),(6,10),(7,4),(7,5),(7,6),(8,15),(9,11),(9,15),(10,12),(10,15),(11,14),(12,14),(13,2),(14,13),(15,1),(15,14)],16)
=> ?
=> ? = 13 + 1
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ([(0,7),(2,11),(2,12),(3,8),(4,10),(4,13),(5,9),(5,13),(6,2),(6,9),(6,10),(7,4),(7,5),(7,6),(8,14),(9,11),(9,16),(10,12),(10,16),(11,15),(12,15),(13,3),(13,16),(14,1),(15,14),(16,8),(16,15)],17)
=> ?
=> ? = 13 + 1
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ([(0,7),(2,9),(2,10),(3,8),(3,10),(4,8),(4,9),(5,1),(6,5),(7,2),(7,3),(7,4),(8,11),(9,11),(10,11),(11,6)],12)
=> ?
=> ? = 11 + 1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
=> ([(0,9),(1,5),(2,9),(2,10),(3,7),(3,10),(4,6),(4,8),(5,7),(6,9),(6,10),(7,8),(8,10)],11)
=> ? = 8 + 1
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
=> ?
=> ? = 9 + 1
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ([(0,7),(2,8),(3,9),(3,11),(4,9),(4,10),(5,1),(6,3),(6,4),(6,8),(7,2),(7,6),(8,10),(8,11),(9,12),(10,12),(11,12),(12,5)],13)
=> ?
=> ? = 11 + 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> ?
=> ? = 7 + 1
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ([(0,7),(2,10),(3,9),(4,3),(4,8),(5,2),(5,8),(6,1),(7,4),(7,5),(8,9),(8,10),(9,11),(10,11),(11,6)],12)
=> ?
=> ? = 9 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ([(0,7),(1,10),(3,8),(4,9),(5,4),(5,11),(6,5),(6,8),(7,3),(7,6),(8,11),(9,10),(10,2),(11,1),(11,9)],12)
=> ?
=> ? = 9 + 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ([(0,7),(2,11),(3,10),(4,9),(5,6),(5,11),(6,4),(6,8),(7,2),(7,5),(8,9),(8,10),(9,12),(10,12),(11,3),(11,8),(12,1)],13)
=> ?
=> ? = 9 + 1
Description
The number of positive eigenvalues of the Laplacian matrix of the graph.
This is the number of vertices minus the number of connected components of the graph.
The following 15 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000453The number of distinct Laplacian eigenvalues of a graph. St000636The hull number of a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001342The number of vertices in the center of a graph. St001356The number of vertices in prime modules of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001672The restrained domination number of a graph. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!