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- W3095853448 abstract "In addition to the unique cover $M^+$ of the variety of modular lattices, we also deal with those twenty-three known covers of $M^+$ that can be extracted from the literature. For $M^+$ and for each of these twenty-three known varieties covering it, we determine what the pair formed by the number of atoms and that of coatoms of a three-generated lattice belonging to the variety in question can be. Furthermore, for each variety $W$ of lattices that is obtained by forming the join of some of the twenty-three varieties mentioned above, that is, for $2^{23}$ possible choices of $W$, we determine how many atoms a three-generated lattice belonging to $W$ can have. The greatest number of atoms occurring in this way is only six. In order to point out that this need not be so for larger varieties, we construct a $47,092$-element three-generated lattice that has exactly eighteen atoms. In addition to purely lattice theoretical proofs, which constitute the majority of the paper, some computer-assisted arguments are also presented." @default.
- W3095853448 created "2020-11-09" @default.
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- W3095853448 date "2022-08-30" @default.
- W3095853448 modified "2023-09-27" @default.
- W3095853448 title "Atoms and coatoms in three-generated lattices" @default.
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- W3095853448 doi "https://doi.org/10.30755/nsjom.12402" @default.
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