Generating Modular Lattices of up to 30 Elements

Research output: Contribution to journalArticle

Details

Original languageEnglish
JournalOrder
StateE-pub ahead of print - 1 Jan 2018
MoE publication typeA1 Journal article-refereed

Researchers

  • Jukka Kohonen

Research units

  • University of Helsinki

Abstract

An algorithm is presented for generating finite modular, semimodular, graded, and geometric lattices up to isomorphism. Isomorphic copies are avoided using a combination of the general-purpose graph-isomorphism tool nauty and some optimizations that handle simple cases directly. For modular and semimodular lattices, the algorithm prunes the search tree much earlier than the method of Jipsen and Lawless, leading to a speedup of several orders of magnitude. With this new algorithm modular lattices are counted up to 30 elements, semimodular lattices up to 25 elements, graded lattices up to 21 elements, and geometric lattices up to 34 elements. Some statistics are also provided on the typical shape of small lattices of these types.

    Research areas

  • Counting algorithm, Geometric lattices, Graded lattices, Modular lattices, Semimodular lattices

ID: 28770605