Catalogue of unlabelled lattices on up to 16 elements

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).

本数据集的目录文件均为纯文本文件（较大文件已采用xz格式压缩）。其中unlabelled-N.cats文件包含了含N个元素的无标号格（unlabelled lattices）的同构类（isomorphism classes）代表元，文件中每一行对应一个格，行末以换行符'
'（即0x0a）结束。单个格的行编码规则如下：将格的元素标记为1, 2, …, N，其中1为该格的上界，N为该格的下界。所选代表元均经过层级化处理：若元素A覆盖元素B（1 ≤ A, B ≤ N），则必有A < B。由此，描述覆盖关系（covering relation）的关联矩阵（incidence matrix）为上三角矩阵（upper triangular matrix）。编码格的行以列主序（column major order）给出该格覆盖关系的关联矩阵（incidence matrix）：对于1 ≤ A < B ≤ N，该行第((B-1)*(B-2)/2 + A)个字符用于标识A是否覆盖B；若A覆盖B，则该字符为'1'，否则为'.'。每个文件内的所有行均按字典序（lexicographical order）排序。若使用本目录中的数据集，请引用以下待发表论文：V. Gebhardt、S. Tawn：《构造无标号格（Constructing unlabelled lattices）》，《代数学刊（Journal of Algebra）》，即将刊出（预计2019年）。