An inductive algorithm to construct finite lattices
Shoji Kyuno · Mathematics of Computation · 1979
G. Birkhoff [1] proposed the following problem: Enumerate all finite lattices which are uniquely determined (up to isomorphism) by their diagram, considered as a graph. It is not known how many lattices of order n exist, except when the value of n is quite small. The aim of this note is to give an algorithm to construct inductively all finite lattices of order n . Using this algorithm, we have found that there exist 222 lattices for n = 8 n = 8 and 1078 lattices for n = 9 n = 9 . All lattices of order n ⩽ 8 n \leqslant 8 are shown at the end of this note.