Identifier
Mp00195: Posets order idealsLattices
Mp00191: Lattices dual Lattices
Images
=>
Cc0014;cc-rep-0Cc0029;cc-rep-1Cc0029;cc-rep-2
([],1)=>([(0,1)],2)=>([(0,1)],2) ([],2)=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4) ([(0,1)],2)=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3) ([],3)=>([(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) ([(1,2)],3)=>([(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) ([(0,1),(0,2)],3)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) ([(0,2),(2,1)],3)=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4) ([(0,2),(1,2)],3)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) ([],4)=>([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)=>([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16) ([(2,3)],4)=>([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)=>([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12) ([(1,2),(1,3)],4)=>([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)=>([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10) ([(0,1),(0,2),(0,3)],4)=>([(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)=>([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9) ([(0,2),(0,3),(3,1)],4)=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) ([(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) ([(1,2),(2,3)],4)=>([(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) ([(0,3),(3,1),(3,2)],4)=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) ([(1,3),(2,3)],4)=>([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)=>([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10) ([(0,3),(1,3),(3,2)],4)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) ([(0,3),(1,3),(2,3)],4)=>([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],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) ([(0,3),(1,2)],4)=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) ([(0,3),(1,2),(1,3)],4)=>([(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) ([(0,2),(0,3),(1,2),(1,3)],4)=>([(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) ([(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) ([(0,3),(1,2),(2,3)],4)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) ([(2,3),(2,4)],5)=>([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)=>([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20) ([(1,2),(1,3),(1,4)],5)=>([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18) ([(0,1),(0,2),(0,3),(0,4)],5)=>([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)=>([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17) ([(0,2),(0,3),(0,4),(4,1)],5)=>([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)=>([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13) ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)=>([(0,4),(0,5),(2,7),(2,9),(3,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,8),(6,9),(7,10),(8,10),(9,10),(10,1)],11) ([(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) ([(1,3),(1,4),(4,2)],5)=>([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14)=>([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,1),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8)],14) ([(0,3),(0,4),(4,1),(4,2)],5)=>([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)=>([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11) ([(1,2),(1,3),(2,4),(3,4)],5)=>([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)=>([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12) ([(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)=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) ([(0,3),(0,4),(3,2),(4,1)],5)=>([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)=>([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)=>([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9) ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) ([(2,3),(3,4)],5)=>([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)=>([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16) ([(1,4),(4,2),(4,3)],5)=>([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)=>([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12) ([(0,4),(4,1),(4,2),(4,3)],5)=>([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)=>([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10) ([(2,4),(3,4)],5)=>([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)=>([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20) ([(1,4),(2,4),(4,3)],5)=>([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)=>([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12) ([(0,4),(1,4),(4,2),(4,3)],5)=>([(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) ([(1,4),(2,4),(3,4)],5)=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)=>([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18) ([(0,4),(1,4),(2,4),(4,3)],5)=>([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)=>([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10) ([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)=>([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17) ([(0,4),(1,4),(2,3)],5)=>([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)=>([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15) ([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)=>([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13) ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)=>([(0,4),(0,5),(1,7),(1,9),(2,7),(2,8),(3,6),(4,10),(5,3),(5,10),(6,8),(6,9),(7,11),(8,11),(9,11),(10,1),(10,2),(10,6)],12) ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)=>([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11) ([(0,4),(1,4),(2,3),(4,2)],5)=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) ([(0,4),(1,3),(2,3),(3,4)],5)=>([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)=>([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11) ([(0,4),(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)=>([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14) ([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)=>([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13) ([(1,4),(2,3)],5)=>([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)=>([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18) ([(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)=>([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16) ([(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)=>([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11) ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)=>([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9) ([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)=>([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14) ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)=>([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9) ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) ([(0,4),(1,2),(1,4),(4,3)],5)=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10) ([(0,4),(1,2),(1,3)],5)=>([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15)=>([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15) ([(0,4),(1,2),(1,3),(1,4)],5)=>([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)=>([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14) ([(0,2),(0,4),(3,1),(4,3)],5)=>([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)=>([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) ([(0,4),(1,2),(1,3),(3,4)],5)=>([(0,4),(0,5),(1,8),(2,7),(2,9),(3,7),(3,10),(4,6),(5,2),(5,3),(5,6),(6,9),(6,10),(7,11),(9,11),(10,1),(10,11),(11,8)],12)=>([(0,4),(0,5),(1,8),(2,7),(2,9),(3,7),(3,10),(4,6),(5,2),(5,3),(5,6),(6,9),(6,10),(7,11),(9,11),(10,1),(10,11),(11,8)],12) ([(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) ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,4),(0,5),(2,7),(2,9),(3,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,8),(6,9),(7,10),(8,10),(9,10),(10,1)],11)=>([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11) ([(0,3),(0,4),(1,2),(1,4)],5)=>([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13)=>([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13) ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>([(0,4),(0,5),(1,7),(1,9),(2,7),(2,8),(3,6),(4,10),(5,3),(5,10),(6,8),(6,9),(7,11),(8,11),(9,11),(10,1),(10,2),(10,6)],12)=>([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12) ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11) ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)=>([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10) ([(0,3),(1,2),(1,4),(3,4)],5)=>([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)=>([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11) ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)=>([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9) ([(1,4),(3,2),(4,3)],5)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) ([(0,3),(3,4),(4,1),(4,2)],5)=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) ([(1,4),(2,3),(3,4)],5)=>([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,1),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8)],14)=>([(0,1),(0,2),(1,11),(2,3),(2,4),(2,11),(3,8),(3,10),(4,5),(4,9),(4,10),(5,6),(5,7),(6,13),(7,13),(8,12),(9,7),(9,12),(10,6),(10,12),(11,8),(11,9),(12,13)],14) ([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) ([(0,3),(1,4),(4,2)],5)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) ([(0,4),(3,2),(4,1),(4,3)],5)=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) ([(0,4),(1,2),(2,3),(2,4)],5)=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10) ([(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) ([(0,3),(1,2),(2,4),(3,4)],5)=>([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)=>([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10) ([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)=>([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9) ([(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)=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9)=>([(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(7,6),(8,1)],9) ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,5)],9)=>([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,5)],9) ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)=>([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8) ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>([(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(7,6),(8,1)],9)=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9) ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) ([(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)=>([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9) ([(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)=>([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8) ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)=>([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) ([(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) ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)=>([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) ([(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) ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)=>([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9) ([(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)=>([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8) ([(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)=>([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9) ([(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),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9) ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>([(0,2),(0,3),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,7)],9)=>([(0,6),(1,8),(2,8),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],9) ([(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)=>([(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2),(8,3)],9) ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)=>([(0,6),(1,8),(2,8),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],9)=>([(0,2),(0,3),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,7)],9) ([(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) ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(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) ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>([(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2),(8,3)],9)=>([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal $\mathcal I$ in a poset $P$ is a downward closed set, i.e., $a \in \mathcal I$ and $b \leq a$ implies $b \in \mathcal I$. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
Map
dual
Description
Return the dual lattice.
The dual (or opposite) of a lattice $(\mathcal P,\leq)$ is the lattice $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.