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- W4298051846 abstract "We present explicit constructions of centrally symmetric polytopes with many faces: first, we construct a d-dimensional centrally symmetric polytope P with about (1.316)^d vertices such that every pair of non-antipodal vertices of P spans an edge of P, second, for an integer k>1, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < delta_k < 1 at least (1-delta_k^d) {N choose k} k-subsets of the set of vertices span faces of P, and third, for an integer k>1 and a>0, we construct a centrally symmetric polytope Q with an arbitrary large number N of vertices and of dimension d=k^{1+o(1)} such that least (1 - k^{-a}){N choose k} k-subsets of the set of vertices span faces of Q." @default.
- W4298051846 created "2022-10-01" @default.
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- W4298051846 date "2011-06-02" @default.
- W4298051846 modified "2023-09-25" @default.
- W4298051846 title "Centrally symmetric polytopes with many faces" @default.
- W4298051846 doi "https://doi.org/10.48550/arxiv.1106.0449" @default.
- W4298051846 hasPublicationYear "2011" @default.
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