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arXiv · 1810.01528

Meet-Distributive Lattices have the Intersection Property

Henri Mühle
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Abstract

Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join semidistributive. Therefore, they admit two natural, secondary structures: the core label order is an alternative order on the lattice elements and the canonical join complex is the flag-simplicial complex on canonical join representations. In this article we present a characterization of finite meet-distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite meet-distributive lattice is always a meet-semilattice.

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Henri Mühle. 2021-06-05. Meet-Distributive Lattices have the Intersection Property. https://doi.org/10.21136/mb.2022.0072-21

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