Counting Regions With Bounded Surface Area
نویسنده
چکیده
Define a cubical complex to be a collection of integer-aligned unit cubes in d dimensions. Lebowitz and Mazel (1998) proved that there are between (C1d) and (C2d) complexes containing a fixed cube with connected boundary of (d − 1)volume n. In this paper we narrow these bounds to between (C3d) and (C4d). We also show that there are nn/(2d(d−1))+o(1) connected complexes containing a fixed cube with (not necessarily connected) boundary of volume n.
منابع مشابه
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— Manin’s conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin’s conjecture for a singular quartic del Pezzo surface.
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— Manin’s conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin’s conjecture for a singular quartic del Pezzo surface.
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