G'abor Cz'edli

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math.CO2023

Minimum-sized generating sets of the direct powers of free distributive lattices

Gábor Czédli

For a finite lattice $L$ , let Gm( $L$ ) denote the least $n$ such that $L$ can be generated by $n$ elements. For integers $r > 2$ and $k > 1$ , denote by FD $(r)^{k}$ the $k$ -th direct power…

math.CO2023

Sperner theorems for unrelated copies of some partially ordered sets in a powerset lattice and minimum generating sets of powers of distributive lattices

Gábor Czédli

For a finite poset (partially ordered set) $U$ and a natural number $n$ , let Sp $(U, n)$ denote the largest number of pairwise unrelated copies of $U$ in the powerset lattice (AKA su…