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The order dimension of multinomial lattices. (English) Zbl 0795.06004

Summary: Using the notion of Ferrers dimension of incidence structures, the order dimension of multinomial lattices (i.e. lattices of ‘multi-permutations’) is determined. In particular, it is shown that the lattice of all permutations on an \(n\)-element set has dimension \(n-1\).

MSC:

06B23 Complete lattices, completions
05A05 Permutations, words, matrices
06A07 Combinatorics of partially ordered sets
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