On the convex hull of the integer points in a disc

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On the convex hull of the integer points in a disc

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Annual Symposium on Computational Geometry archive
Proceedings of the seventh annual symposium on Computational geometry table of contents

North Conway, New Hampshire, United States

Pages: 162 - 165

Year of Publication: 1991

ISBN:0-89791-426-0

Authors

Antal Balog	Institute for Advanced Study, Princeton, NJ
Imre Bárány	Yale University, New Haven, CT and NYU, New York, NY

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 4, Downloads (12 Months): 15, Citation Count: 3

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	G.E. Andrews, A lower bound for the volumes of strictly convex bodies with many boundary points, Trans. Amer. Math. Soc., 106 (1963), 270-279.
	2	V.I. Arnold, Statistics of integral convex polytopes (in Russian), FunctionalAnal. Appl., 14 (1980), 1-3.
	3	I. Bfirfiny, R. Howe, L. Lovfisz, On integer points in polyhedra: A lower bound, to appear in Combinatorica (1991).
	4	J. R. Chert, The lattice points in a circle, Sci. Sinica, 12 (1963), 633-649.
	5	W. Cook, M. Hartman, R. Kannan, C. McDiarmid, On integer points in polyhedra, to appear in Combinatorica (1991).
	6	J. G. van der Corput, Verscharfung der Abschatzung beim Teilerproblem, Math. Annalen, 87 (1922), 39-65.
	7	F. Fricker, Einfiihrung in die Gitterpunktlehre, BirkhSuser, Basel-Boston-Stuttgart, 1982.
	8	M.N. Huxley, Exponential sums and lattice points, Proc. London Math. Soc. (3), 60 (1990), 471-502.
	9	V. Jarnik, Uber Gitterpunkte and konvex Kurven, Math. Zeitschrifi, 24 (1925), 500-518.
	10	S.B. Konyagin, K. A. Sevastyanov, }Estimation of the number of vertices of a convex integral polyhedron in terms of its volume (in Russian), Funktional Anal. Appl., 18 (1984), 13-15.
	11	R. Schneider, Random approximation of convex sets, Microscopy, 151 (1988), 211-227.
	12	W.M. Schmidt, Integer points on curves and surfaces, Monatshdfie fdr Math., 99 (1985), 45-72.
	13	H. P. F. Swinnerton-Dyer, The number of lattice points on a convex curve, .t. Number Theory, 6 (1974), 128-135.
	14	I.M. Vinogradov, On the number of integer points in a sphere (in Russian), lzv. Akad. Nauk SSSR, Ser. Mat., 27 (1963), 957-968.
	15	A. Waltisz, GitterpunMe in mehrdimensionalischen Ku geln, Panstwowe Wydawnictwo Naukowe , Warszawa, 1957.

CITED BY 4

	William Hesse, Directed graphs requiring large numbers of shortcuts, Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, January 12-14, 2003, Baltimore, Maryland
	François de Vieilleville , Jacques-Olivier Lachaud, Comparison and improvement of tangent estimators on digital curves, Pattern Recognition, v.42 n.8, p.1693-1707, August, 2009
	François De Vieilleville , Jacques-Olivier Lachaud , Fabien Feschet, Convex Digital Polygons, Maximal Digital Straight Segments and Convergence of Discrete Geometric Estimators, Journal of Mathematical Imaging and Vision, v.27 n.2, p.139-156, February 2007
	Sariel Har-Peled, An output sensitive algorithm for discrete convex hulls, Proceedings of the fourteenth annual symposium on Computational geometry, p.357-364, June 07-10, 1998, Minneapolis, Minnesota, United States