Multipasting of lattices
A new lattice construction called multipasting is introduced; this generalizes the constructions of gluing, pasting and \(S\)-glued sum, which were investigated in several papers. A multipasting of a family of lattices \(L_ \lambda\) \((\lambda\in\Lambda)\) is a lattice \(L\) such that all \(L_ \lambda\) are sublattices of \(L\) satisfying certain conditions (the detailed definition would be too lengthy to be reproduced here). By using the notion of \(\Sigma\)-pasting it is proved that multipasting can be in fact treated as a construction, thus the family \(L_ \lambda\) \((\lambda\in\Lambda)\) of lattices can be arbitrary. The relations between multipasting and the above-mentioned types of constructions are studied. Next, by applying stronger sets of conditions, the authors define and investigate the notions of (i) strong multipasting, (ii) multipasting of convex sublattices, and (iii) multipasting with the (upper) interpolation property. The results on strong multipasting concern lattices of finite length. Some open problems are proposed.
scientific article; zbMATH DE number 203152
scientific article