Flath, Sigrid The order dimension of multinomial lattices. (English) Zbl 0795.06004 Order 10, No. 3, 201-219 (1993). 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 \(n-1\). Cited in 3 ReviewsCited in 5 Documents MSC: 06B23 Complete lattices, completions 05A05 Permutations, words, matrices 06A07 Combinatorics of partially ordered sets Keywords:permutation lattice; formal concept analysis; Ferrers dimension; incidence structures; order dimension; multinomial lattices PDF BibTeX XML Cite \textit{S. Flath}, Order 10, No. 3, 201--219 (1993; Zbl 0795.06004) Full Text: DOI OpenURL References: [1] M. K. Bennett and G. Birkhoff (1991) Two families of Newman lattices, Preprint, to appear inAlgebra Universalis. · Zbl 0810.06006 [2] A. Bouchet (1971) Etude combinatoire des ordonnés finis: Applications, Thèse de Doctorat d’Etat, Univ. Sci. et Méd., Grenoble. [3] O. Cogis (1980) La dimension Ferrers des graphes orientés, Thèse, Université Pierre et Marie Curie, Paris. [4] M. H. A. Newman (1942) On theories with a combinatorial definition of equivalence,Annals of Math. 43, 223-243. · Zbl 0060.12501 [5] K. Reuter (1989) On the dimension of the Cartesian product of relations and orders,Order 6, 277-293. · Zbl 0699.06004 [6] R. Wille (1982) Restructuring lattice theory: An approach based on hierarchies of concepts, inOrdered Sets (ed. I. Rival), D. Reidel, Dordrecht, 445-470. [7] R. Wille (1985) Tensorial decompositions of concept lattices,Order 2, 81-95. · Zbl 0583.06007 [8] R. Wille (1989) Lattices in data analysis: How to draw them with a computer, inAlgorithms and Order (ed. I. Rival), KAP, Dordrecht, 33-58. · Zbl 1261.68140 [9] T. Yanagimoto and M. Okamoto (1969) Partial orderings of permutations and monotonicity of a rank correlation statistic,Ann. Inst. Statist. Math. 21, 489-506. · Zbl 0208.44704 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.