Realization of posets

Patrice Ossona de Mendez (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

We prove a very general representation theorem for posets and, as a corollary, deduce that any abstract simplicial complex S has a geometric realization in the Euclidean space of dimension P(S)-1, where P(S) is the Dushnik-Miller dimension of the face order of S.

Mots clés: poset dimension; geometric convexity

Domaines: Combinatoire [math.CO]

Patrice Ossona de Mendez. Realization of posets. Journal of Graph Algorithms and Applications, 2002, 6(1), pp.149-153. ⟨hal-00005629⟩