Generating Modular Lattices of up to 30 Elements

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • University of Helsinki

Kuvaus

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.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut423–435
JulkaisuOrder
Vuosikerta36
Numero3
Varhainen verkossa julkaisun päivämäärä1 tammikuuta 2018
TilaJulkaistu - marraskuuta 2019
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 28770605