Footnote:
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Description:
The topic of this thesis are subdivisions of simplicial complexes, in particular we focus on the so-called antiprism triangulation. In the first main part, the real-rootedness of the h-polynomial of the antiprism triangulation of the simplex is proven. Furthermore, we study combinatorial interpretations of several invariants as the h- and local h-vector. In the second part, we show the almost strong Lefschetz property of the antiprism triangulation for every shellable simplicial complex.