The lattice of partitions of a positive integer (Q960662)

The authors introduce a natural lattice order on the set NPL\((n)\) of all partitions of a given positive integer \(n\). The set NPL of partitions of all positive integers is endowed with a lattice order as well. Also fast algorithms are suggested for constructing meets and joins of eleuents in the lattices of partitions. The introduced lattice order on NPL\((n)\) is known as the ordering of dominance or majorization, cf. \textit{T. Brylawski} [Discrete Math. 6, 201--219 (1973; Zbl 0283.06003)]; \textit{C. Greene} and \textit{D. Kleitman} [Eur. J. Comb. 7, 1--10 (1986; Zbl 0605.05003)].