Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001651
Mapping
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00047: Ordered trees —to poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001651: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [[]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 0
[1,1,0,0]
 => [[[]]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[1,0,1,1,0,0]
 => [[],[[]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 0
[1,1,0,0,1,0]
 => [[[]],[]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 0
[1,1,1,0,0,0]
 => [[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[1,0,1,0,1,1,0,0]
 => [[],[],[[]]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 0
[1,0,1,1,0,0,1,0]
 => [[],[[]],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 0
[1,0,1,1,1,0,0,0]
 => [[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
[1,1,0,0,1,0,1,0]
 => [[[]],[],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 0
[1,1,0,0,1,1,0,0]
 => [[[]],[[]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
[1,1,0,1,1,0,0,0]
 => [[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => 0
[1,1,1,0,0,0,1,0]
 => [[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
[1,1,1,0,0,1,0,0]
 => [[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => 0
[1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 3
[1,0,1,0,1,0,1,1,0,0]
 => [[],[],[],[[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[],[],[[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [[],[[]],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[],[[]],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [[[]],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[[]],[],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[[]],[[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[[]],[[],[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[[]],[[[]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
[1,1,0,1,0,0,1,1,0,0]
 => [[[],[]],[[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[[],[],[[]]]]
 => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[[],[[]]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,1,0,1,1,0,0,1,0,0]
 => [[[],[[]],[]]]
 => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[[],[[[]]]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [[[[]]],[],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[[[]]],[[]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2
[1,1,1,0,0,1,0,0,1,0]
 => [[[[]],[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,1,1,0,0,1,0,1,0,0]
 => [[[[]],[],[]]]
 => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,1,1,0,0,1,1,0,0,0]
 => [[[[]],[[]]]]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
[1,1,1,0,1,1,0,0,0,0]
 => [[[[],[[]]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,1,1,1,0,0,0,0,1,0]
 => [[[[[]]]],[]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [[[[[]]],[]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
[1,1,1,1,0,0,1,0,0,0]
 => [[[[[]],[]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ([(0,1)],2)
 => 0
[1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 4
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [[],[],[],[],[[]]]
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1)],2)
 => 0
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [[],[],[],[[]],[]]
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1)],2)
 => 0
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [[],[],[],[[[]]]]
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[],[],[[]],[],[]]
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,1)],2)
 => 0
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[],[],[[]],[[]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [[],[],[[],[[]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,1)],2)
 => 0
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [[],[],[[[]]],[]]
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => 1
Description
The Frankl number of a lattice. For a lattice $L$ on at least two elements, this is $$ \max_x(|L|-2|[x, 1]|), $$ where we maximize over all join irreducible elements and $[x, 1]$ denotes the interval from $x$ to the top element. Frankl's conjecture asserts that this number is non-negative, and zero if and only if $L$ is a Boolean lattice.
Matching statistic: St001207
(load all 3 compositions to match this statistic)
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 22%
Values
[1,0]
 => []
 => []
 => [] => ? = 0 + 1
[1,1,0,0]
 => []
 => []
 => [] => ? = 1 + 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1 = 0 + 1
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,1,3] => 1 = 0 + 1
[1,1,1,0,0,0]
 => []
 => []
 => [] => ? = 2 + 1
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 1 = 0 + 1
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 1 = 0 + 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,4,2,3] => 2 = 1 + 1
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 1 = 0 + 1
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 1 = 0 + 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1 = 0 + 1
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => 2 = 1 + 1
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,1,3] => 1 = 0 + 1
[1,1,1,1,0,0,0,0]
 => []
 => []
 => [] => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,3,4] => ? = 1 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,2,4] => ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,4,2,3,5] => ? = 1 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4,2,5,3] => ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,2,3,4] => ? = 2 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,3,4] => ? = 2 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [2,4,1,3,5] => ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,4,2,3] => 2 = 1 + 1
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,1,2,4,5] => ? = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,1,2,5,4] => ? = 2 + 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [3,1,4,2,5] => ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 1 = 0 + 1
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [4,1,2,3,5] => ? = 2 + 1
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => 2 = 1 + 1
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,1,3] => 1 = 0 + 1
[1,1,1,1,1,0,0,0,0,0]
 => []
 => []
 => [] => ? = 4 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,4,6,5] => ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => ? = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [3,3,3,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,2,3,6,4,5] => ? = 1 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => ? = 0 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,2,4,3,6,5] => ? = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,2,4,6,3,5] => ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [5,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,2,5,3,4,6] => ? = 1 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [4,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,5,3,6,4] => ? = 0 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,2,6,3,4,5] => ? = 2 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => ? = 0 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [4,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,3,2,4,6,5] => ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [5,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4,6] => ? = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [4,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,3,2,5,6,4] => ? = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [3,3,3,1,1]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,6,4,5] => ? = 2 + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [4,4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,4,2,6,5] => ? = 0 + 1
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [3,3,2,1,1]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,3,4,6,2,5] => ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [5,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,3,5,2,4,6] => ? = 0 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [4,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,3,5,2,6,4] => ? = 0 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,3,6,2,4,5] => ? = 1 + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,4,2,3,5,6] => ? = 1 + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [4,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,4,2,3,6,5] => ? = 2 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,4,2,5,3,6] => ? = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,4,2,5,6,3] => ? = 0 + 1
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [3,3,1,1,1]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,4,2,6,3,5] => ? = 0 + 1
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,4,6,2,3,5] => ? = 0 + 1
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => 1 = 0 + 1
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,4,2,3] => 2 = 1 + 1
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => 1 = 0 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,1,4,3] => 1 = 0 + 1
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1 = 0 + 1
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => 2 = 1 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,1,3] => 1 = 0 + 1
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.