2016/09/30 by Volker Gebhardt, Stephen Tawn · 1 citation
Computer Science · Materials Science · Mathematics · #Copper Interconnects and Reliability #Rough Sets and Fuzzy Logic #cs.DM #math.CO #math.GR #msc:05-04 #msc:05A15 #msc:06A07 #semigroups and automata theory
paper · pdf · doi:10.1016/j.jalgebra.2018.10.017
published as Journal of Algebra 545 (2020) 213-236 · 22 pages; published version
arxiv created 2019/12/20 · arxiv updated 2019/12/23
We present an improved orderly algorithm for constructing all unlabelled lattices up to a given size, that is, an algorithm that constructs the minimal element of each isomorphism class relative to some total order. Our algorithm employs a stabiliser chain approach for cutting branches of the search space that cannot contain a minimal lattice; to make this work, we grow lattices by adding a new layer at a time, as opposed to adding one new element at a time, and we use a total order that is compatible with this modified strategy. The gain in speed is between one and two orders of magnitude. As an application, we compute the number of unlabelled lattices on 20 elements.