Abstract
We characterize lattices obtained from another lattice by a doubling of a convex set. This gives rise to a characterization of the class CN of lattices obtained by doublings of connected and convex sets when starting from a two-element lattice, and from this characterization result we derive an efficient recognition algorithm. This algorithm can be directly applied to the recognition of lattices in the subclasses of CN defined by giving some additionnal constraints on the convex sets used in the doublings.
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Bertet, K., Caspard, N. Doubling Convex Sets in Lattices: Characterizations and Recognition Algorithms. Order 19, 181–207 (2002). https://doi.org/10.1023/A:1016524118566
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DOI: https://doi.org/10.1023/A:1016524118566