A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes
نویسندگان
چکیده
منابع مشابه
On the number of faces of centrally-symmetric simplicial polytopes
I. Bfirfiny and L. Lovfisz [Acta Math. Acad. Sci. Hung. 40, 323-329 (1982)] showed that a d-dimensional centrally-symmetric simplicial polytope ~ has at least 2 d facets, and conjectured a lower bound for the number f~ of i-dimensional faces o f ~ in terms ofd and the number f0 = 2n of d vertices. Define integers ho . . . . . he by Z f~-1(x 1) d-' = ~ hi xd-'. A. Bj6rner conjectured (uni=O i=O ...
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In 1989 Kalai stated the three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture,A, became known as the “3-conjecture”. It is well-known that the three conjectures hold in dimensions d ≤ 3. We show that in dimension 4 only conjectures A and B are valid, while conjecture C fails. Furthermore, we show that both conje...
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Let S(n, d) and C(n, d) denote, respectively, the stacked and the cyclic d-dimensional polytopes on n vertices. Furthermore, fi(P ) denotes the number of i-dimensional faces of a polytope P . Theorem 1. Let P be a d-dimensional simplicial polytope. Suppose that fr(S(n1, d)) ≤ fr(P ) ≤ fr(C(n2, d)) for some integers n1, n2 and r ≤ d − 2. Then, fs(S(n1, d)) ≤ fs(P ) ≤ fs(C(n2, d)) for all s such ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2018
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-018-9978-z