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• W3036200086 abstract "The antiprism triangulation provides a natural way to subdivide a simplicial complex $Delta$, similar to barycentric subdivision, which appeared independently in combinatorial algebraic topology and computer science. It can be defined as the simplicial complex of chains of multi-pointed faces of $Delta$, from a combinatorial point of view, and by successively applying the antiprism construction, or balanced stellar subdivisions, on the faces of $Delta$, from a geometric point of view. This paper studies enumerative invariants associated to this triangulation, such as the transformation of the $h$-vector of $Delta$ under antiprism triangulation, and algebraic properties of its Stanley--Reisner ring. Among other results, it is shown that the $h$-polynomial of the antiprism triangulation of a simplex is real-rooted and that the antiprism triangulation of $Delta$ has the almost strong Lefschetz property over ${mathbb R}$ for every shellable complex $Delta$. Several related open problems are discussed." @default.
• W3036200086 created "2020-06-25" @default.
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• W3036200086 date "2020-06-18" @default.
• W3036200086 modified "2023-09-27" @default.
• W3036200086 title "Combinatorics of antiprism triangulations" @default.
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