Exponential lower bounds of lattice counts by vertical sum and 2-sum

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dc.contributor University of Helsinki, Department of Computer Science en
dc.contributor.author Kohonen, Jukka
dc.date.accessioned 2019-08-27T07:47:01Z
dc.date.available 2019-08-27T07:47:01Z
dc.date.issued 2019-03
dc.identifier.citation Kohonen , J 2019 , ' Exponential lower bounds of lattice counts by vertical sum and 2-sum ' , Algebra Universalis , vol. 80 , no. 1 , 13 . https://doi.org/10.1007/s00012-019-0586-4 en
dc.identifier.issn 0002-5240
dc.identifier.other PURE: 123264148
dc.identifier.other PURE UUID: 299c072d-9d2e-4590-8d0c-0357ac1037df
dc.identifier.other WOS: 000459471500001
dc.identifier.other Scopus: 85062023767
dc.identifier.uri http://hdl.handle.net/10138/304957
dc.description.abstract We consider the problem of finding lower bounds on the number of unlabeled n-element lattices in some lattice family. We show that if the family is closed under vertical sum, exponential lower bounds can be obtained from vertical sums of small lattices whose numbers are known. We demonstrate this approach by establishing that the number of modular lattices is at least 2.2726n for n large enough. We also present an analogous method for finding lower bounds on the number of vertically indecomposable lattices in some family. For this purpose we define a new kind of sum, the vertical 2-sum, which combines lattices at two common elements. As an application we prove that the numbers of vertically indecomposable modular and semimodular lattices are at least 2.1562n and 2.6797n for n large enough. en
dc.format.extent 11
dc.language.iso eng
dc.relation.ispartof Algebra Universalis
dc.rights en
dc.subject Modular lattices en
dc.subject Semimodular lattices en
dc.subject Vertical sum en
dc.subject Vertical 2-sum en
dc.subject Counting en
dc.subject 111 Mathematics en
dc.title Exponential lower bounds of lattice counts by vertical sum and 2-sum en
dc.type Article
dc.description.version Peer reviewed
dc.identifier.doi https://doi.org/10.1007/s00012-019-0586-4
dc.type.uri info:eu-repo/semantics/other
dc.type.uri info:eu-repo/semantics/publishedVersion

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