Counting Finite Lattices

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 2002 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 48, pages 43-53 (issn: 0002-5240,

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Authors: Heitzig, Jobst; Reinhold, Jürgen;

doi: 10.1007/pl00013837

Counting Finite Lattices

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Abstract

The authors present a fast orderly algorithm generating all un(labeled) lattices up to a given size \(n\). Using this algorithm, they compute the number \(l(n)\) of all unlabeled lattices having no more than 18 elements. This result also corrects wrong numbers \(l(11)\) and \(l(12)\) by \textit{Y. Koda} [Bull. Inst. Comb. Appl. 10, 83--89 (1994; Zbl 0806.05005)].

Related Organizations

University of Hannover
Germany

Keywords

Combinatorics of partially ordered sets, orderly algorithm, Exact enumeration problems, generating functions, canonical, lattice, tree

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