Identifier
-
Mp00193:
Lattices
—to poset⟶
Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001884: Binary words ⟶ ℤ
Values
([],1) => ([],1) => [1] => 10 => 1
([(0,1)],2) => ([(0,1)],2) => [2] => 100 => 1
([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => [3] => 1000 => 1
([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => [3,1] => 10010 => 2
([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => [4] => 10000 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,1,1] => 100110 => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [4,1] => 100010 => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [4,1] => 100010 => 2
([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => 100000 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [4,1] => 100010 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => [3,1,1,1] => 1001110 => 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => [4,1,1] => 1000110 => 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => [4,1,1] => 1000110 => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [4,1,1] => 1000110 => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [5,1] => 1000010 => 2
([(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) => [5,1] => 1000010 => 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [5,1] => 1000010 => 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [5,1] => 1000010 => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => [4,1,1] => 1000110 => 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [5,1] => 1000010 => 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [4,1,1] => 1000110 => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => 100100 => 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [4,2] => 100100 => 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => 1000000 => 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [5,1] => 1000010 => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [3,1,1,1,1] => 10011110 => 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => [4,1,1,1] => 10001110 => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => [4,1,1,1] => 10001110 => 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => [4,1,1,1] => 10001110 => 2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => [4,1,1,1] => 10001110 => 2
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => [5,1,1] => 10000110 => 2
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => [5,1,1] => 10000110 => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [5,1,1] => 10000110 => 2
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => [5,1,1] => 10000110 => 2
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => [5,1,1] => 10000110 => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => [5,1,1] => 10000110 => 2
([(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) => [6,1] => 10000010 => 2
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [5,2] => 1000100 => 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [5,2] => 1000100 => 2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => [5,1,1] => 10000110 => 2
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => [5,1,1] => 10000110 => 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [5,1,1] => 10000110 => 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [4,1,1,1] => 10001110 => 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => [5,1,1] => 10000110 => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [5,2] => 1000100 => 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => [4,1,1,1] => 10001110 => 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => [5,1,1] => 10000110 => 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => [4,1,1,1] => 10001110 => 2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => [4,2,1] => 1001010 => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [4,2,1] => 1001010 => 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [6,1] => 10000010 => 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => [5,1,1] => 10000110 => 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => [4,2,1] => 1001010 => 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => [5,1,1] => 10000110 => 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => [4,2,1] => 1001010 => 2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => [4,2,1] => 1001010 => 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => [5,2] => 1000100 => 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [5,2] => 1000100 => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => [5,2] => 1000100 => 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => [4,2,1] => 1001010 => 2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => [4,2,1] => 1001010 => 2
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [6,1] => 10000010 => 2
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => [5,1,1] => 10000110 => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [6,1] => 10000010 => 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => [5,1,1] => 10000110 => 2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => [4,2,1] => 1001010 => 2
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => [5,2] => 1000100 => 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => [6,1] => 10000010 => 2
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [6,1] => 10000010 => 2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => [5,1,1] => 10000110 => 2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [6,1] => 10000010 => 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => [5,2] => 1000100 => 2
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [6,1] => 10000010 => 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => [5,2] => 1000100 => 2
([(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] => 10000000 => 1
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [5,2] => 1000100 => 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [6,1] => 10000010 => 2
([(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) => [6,1] => 10000010 => 2
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => ([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => [5,2,1] => 10001010 => 2
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) => [6,2] => 10000100 => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => [4,1,1,1,1] => 100011110 => 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8) => [4,1,1,1,1] => 100011110 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8) => [5,1,1,1] => 100001110 => 2
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) => [6,2] => 10000100 => 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => [4,2,1,1] => 10010110 => 2
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => [6,2] => 10000100 => 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => [5,3] => 1001000 => 1
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => [6,2] => 10000100 => 2
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8) => [5,3] => 1001000 => 1
([(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] => 10000100 => 2
([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8) => [5,3] => 1001000 => 1
([(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) => [7,1] => 100000010 => 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => [4,2,2] => 1001100 => 2
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [6,2] => 10000100 => 2
([(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] => 100000000 => 1
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9) => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9) => [5,2,2] => 10001100 => 2
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9) => [5,2,1,1] => 100010110 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9) => [5,2,1,1] => 100010110 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9) => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9) => [5,2,1,1] => 100010110 => 2
([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) => [6,3] => 10001000 => 2
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) => [6,3] => 10001000 => 2
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Description
The number of borders of a binary word.
A border of a binary word $w$ is a word which is both a prefix and a suffix of $w$.
A border of a binary word $w$ is a word which is both a prefix and a suffix of $w$.
Map
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Description
Return the poset corresponding to the lattice.
Map
Greene-Kleitman invariant
Description
The Greene-Kleitman invariant of a poset.
This is the partition $(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$, where $c_k$ is the maximum cardinality of a union of $k$ chains of the poset. Equivalently, this is the conjugate of the partition $(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$, where $a_k$ is the maximum cardinality of a union of $k$ antichains of the poset.
This is the partition $(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$, where $c_k$ is the maximum cardinality of a union of $k$ chains of the poset. Equivalently, this is the conjugate of the partition $(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$, where $a_k$ is the maximum cardinality of a union of $k$ antichains of the poset.
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
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