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n-median semilattices |
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| Authors: | Hans-Jürgen Bandelt Melvin F. Janowitz Gerasimos C. Meletiou |
| Affiliation: | (1) Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, D-2000 Hamburg, Germany;(2) Department of Mathematics and Statistics, University of Massachusetts, 01003 Amherst, MA, U.S.A.;(3) Faculty of Agricultural Technology, T.E.I./M. at Arta, P.O. Box 110, GR-47100 Arta, Greece |
| Abstract: | An n-median semilattice (n 3) is a meet-semilattice such that (i) every principal ideal is a distributive lattice and (ii) any n-element set of elements is bounded above whenever each of its (n-1)-element subsets has an upper bound. A 3-median semilattice is thus a median semilattice in the classical sense. In this note we demonstrate how the characteristic features of median semilattices carry over to the more general case of n-median semilattices.Research supported in part by ONR Grant N00014-90-1008. |
| Keywords: | 06A12 |
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