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- W3137065090 abstract "A stacking operation adds a d-simplex on top of a facet of a simplicial d-polytope while maintaining the convexity of the polytope. A stacked d-polytope is a polytope that is obtained from a d-simplex and a series of stacking operations. We show that for a fixed d every stacked d-polytope with n vertices can be realized with nonnegative integer coordinates. The coordinates are bounded by $$O(n^{2log _2(2d)})$$ , except for one axis, where the coordinates are bounded by $$O(n^{3log _2(2d)})$$ . The described realization can be computed with an easy algorithm. The realization of the polytopes is obtained with a lifting technique which produces an embedding on a large grid. We establish a rounding scheme that places the vertices on a sparser grid, while maintaining the convexity of the embedding." @default.
- W3137065090 created "2021-03-29" @default.
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- W3137065090 date "2017-03-21" @default.
- W3137065090 modified "2023-09-26" @default.
- W3137065090 title "Embedding Stacked Polytopes on a Polynomial-Size Grid" @default.
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- W3137065090 doi "https://doi.org/10.1007/s00454-017-9887-6" @default.
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