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- W1991389996 abstract "Let Bn be a hyperball in Rn, n≥2, and denote BZn=Bn∩Zn. Define polyhedral facet complexity of BZn as FC(BZn)=minP{fn−1(P)} where P is an enclosing polyhedron for BZn (i.e., PZ=P∩Zn=BZn) and fn−1(P) is the number of the (n−1)-facets of P. Analogously, define polyhedral vertex complexity of BZn as VC(BZn)=minP{f0(P)} where P is an enclosing polyhedron for BZn and f0(P) is the number of the 0-facets (vertices) of P. Upper bounds for FC(BZn) follow from a well-known bound for the number of facets and vertices of the convex hull of BZn [I. Bárány, D.G. Larman, The convex hull of the integer points in a large ball, Math. Ann. 312 (1998) 167–181]. In this note we provide the first nontrivial lower bounds on FC(BZn) and VC(BZn)." @default.
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- W1991389996 date "2008-10-01" @default.
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- W1991389996 title "On the polyhedral complexity of the integer points in a hyperball" @default.
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- W1991389996 doi "https://doi.org/10.1016/j.tcs.2008.07.014" @default.
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