Boolean packings in Dowling geometries
A Boolean packing of a geometric lattice \(L\) is a partitioning of \(L\) into cover preserving Boolean sublattices such that for each of them the rank of the bottom element is at least the corank of the top element. For \(L\) of rank 3 this amounts to a matching between atoms and coatoms. In the paper under review, it is pointed out that any Boolean packing implies a partition into symmetric chains for the poset of elements of at most half the rank of \(L\). The main contribution is an explicit construction of Boolean packings for Dowling lattices.
scientific article; zbMATH DE number 1235004