Journal of Graph Algorithms and Applications
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Realization of Posets
Vol. 6, no. 1, pp. 149-153, 2002. Regular paper.
Abstract We prove a very general representation theorem for posets and, as a corollary, deduce that any abstract simplicial complex has a geometric realization in the Euclidean space of dimension dimP(∆)−1, where dimP(∆) is the Dushnik-Miller dimension of the face order of ∆.