On r-stacked triangulated manifolds

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.

Keywords

• stackedness
• triangulation
• manifold
• f-vector
• face ring
• [info.info-dm]computer science [cs]/discrete mathematics [cs.dm]