Enumerating Neighborly Polytopes and Oriented Matroids
نویسندگان
چکیده
منابع مشابه
Constructing neighborly polytopes and oriented matroids
A d-polytope P is neighborly if every subset of b d 2 c vertices is a face of P . In 1982, Shemer introduced a sewing construction that allows to add a vertex to a neighborly polytope in such a way as to obtain a new neighborly polytope. With this, he constructed superexponentially many different neighborly polytopes. The concept of neighborliness extends naturally to oriented matroids. Duals o...
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Consider the moment curve in the real Euclidean space R defined parametrically by the map γ : R → R, t → γ(t) = (t, t, . . . , t). The cyclic d-polytope Cd(t1, . . . , tn) is the convex hull of the n, n > d, different points on this curve. The matroidal analogues are the alternating oriented uniform matroids. A polytope [resp. matroid polytope] is called cyclic if its face lattice is isomorphic...
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Neighborly cubical polytopes exist: for any n ≥ d ≥ 2r + 2, there is a cubical convex d-polytope C d whose r-skeleton is combinatorially equivalent to that of the n-dimensional cube. This solves a problem of Babson, Billera & Chan. Kalai conjectured that the boundary ∂C d of a neighborly cubical polytope C n d maximizes the f -vector among all cubical (d− 1)-spheres with 2 vertices. While we sh...
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Simultaneously generalizing both neighborly and neighborly cubical polytopes, we introduce PSN polytopes: their k-skeleton is combinatorially equivalent to that of a product of r simplices. We construct PSN polytopes by three different methods, the most versatile of which is an extension of Sanyal & Ziegler’s “projecting deformed products” construction to products of arbitrary simple polytopes....
متن کاملNeighborly Cubical Polytopes and Spheres
We prove that the neighborly cubical polytopes studied by Günter M. Ziegler and the first author [14] arise as a special case of the neighborly cubical spheres constructed by Babson, Billera, and Chan [4]. By relating the two constructions we obtain an explicit description of a non-polytopal neighborly cubical sphere and, further, a new proof of the fact that the cubical equivelar surfaces of M...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2015
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2015.1015084