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math.RA2024
Atoms in four-element generating sets of partition lattices
Gábor Czédli
Since Henrik Strietz's 1975 paper proving that the lattice Part() of all partitions of an -element finite set is four-generated, more than half a dozen papers have been devot…
math.RA2024
Generating subspace lattices, their direct products, and their direct powers
Gábor Czédli
In 2008, László Zádori proved that the lattice Sub of all subspaces of a vector space of finite dimension at least 3 over a finite field has a 5-element generating set…
math.RA2023
Generating Boolean lattices by few elements and exchanging session keys
Gábor Czédli
Let Sp() denote the number of the -element subsets of a finite -element set. We prove that the least size of a generating subset of the Boolean lattice wi…