Abstract
The notion of $r$-stackedness for simplicial polytopes was introduced by McMullen and Walkup in 1971 as a generalization of stacked polytopes. In this paper, we define the $r$-stackedness for triangulated homology manifolds and study their basic properties. In addition, we find a new necessary condition for face vectors of triangulated manifolds when all the vertex links are polytopal. Généralisant les polytopes simpliciaux empilés, McMullen et Walkup ont introduit en 1971 la notion de $r$-empilement pour les polytopes simpliciaux. Dans cet article, nous définissons la notion de $r$-empilement pour les variétés homologiques simpliciales et étudions ses propriétés élémentaires. En outre, nous donnons une nouvelle condition pour les $f$-vecteurs des variétés simpliciales lorsque tous les sommets ont un lien polytopal.
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