Dataset

Catalogue of unlabelled lattices on up to 16 elements

Western Sydney University
Dr Volker Gebhardt (Principal investigator, Associated with) Dr Stephen Tawn (Associated with)
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ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rfr_id=info%3Asid%2FANDS&rft_id=info:doi10.26183/5bb57347b10a0&rft.title=Catalogue of unlabelled lattices on up to 16 elements&rft.identifier=10.26183/5bb57347b10a0&rft.publisher=Western Sydney University&rft.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).&rft.creator=Dr Volker Gebhardt&rft.date=2018&rft_rights=n/a n/a&rft_rights=CC BY-NC-SA: Attribution-Noncommercial-Share Alike 3.0 AU http://creativecommons.org/licenses/by-nc-sa/3.0/au&rft_subject=Unlabelled Lattice&rft_subject=Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)&rft_subject=Mathematical Sciences&rft_subject=Pure Mathematics&rft_subject=Expanding Knowledge in the Mathematical Sciences&rft_subject=Expanding Knowledge&rft_subject=Expanding Knowledge&rft_subject=Pure Basic Research&rft.type=dataset&rft.language=English Access the data

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Contact Information

Volker Gebhardt (V.Gebhardt@westernsydney.edu.au)

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).

Created: 2018-09-26

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