Catalogue of unlabelled lattices on up to 16 elements

Full description

The catalogue files are plain text files  (The larger files are xz-packed).  The catalogue file unlabelled-N.cats contains representatives of the isomorphism classes of unlabelled lattices with N elements, with each line encoding one lattice. Lines are terminated with '\n' = 0x0a.

Each line of a file encodes one lattice as follows:

• The elements of the lattice are labelled 1,..,N ; where 1 is the upper bound and N is the lower bound of the lattice.

• The chosen representatives are levellised, that is, if A covers B (where 1 ≤ A,B ≤ N), then A < B holds.  Thus, the incidence matrix describing the covering relation is upper triangular.

• The line encoding a lattice gives the incidence matrix for the covering relation of the lattice in column major order: For 1 ≤ A < B ≤ N, the ((B-1)*(B-2)/2+A)-th character of the line indicates whether A covers B; the character is '1' if A covers B; the character is '.' otherwise.

• The lines in each file are sorted lexicographically.

Please cite the following forthcoming paper when using data from this catalogue: V. Gebhardt, S. Tawn: Constructing unlabelled lattices, Journal of Algebra, to appear (due in 2019).