A note on the complexity of real algebraic hypersurfaces

M. Kerber, M. Sagraloff, Graphs and Combinatorics 27 (2011) 419–430.

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Journal Article | Published | English
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Abstract
Given an algebraic hypersurface O in ℝd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3.
Publishing Year
Date Published
2011-03-17
Journal Title
Graphs and Combinatorics
Volume
27
Issue
3
Page
419 - 430
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Kerber M, Sagraloff M. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 2011;27(3):419-430. doi:10.1007/s00373-011-1020-7
Kerber, M., & Sagraloff, M. (2011). A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics, 27(3), 419–430. https://doi.org/10.1007/s00373-011-1020-7
Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” Graphs and Combinatorics 27, no. 3 (2011): 419–30. https://doi.org/10.1007/s00373-011-1020-7.
M. Kerber and M. Sagraloff, “A note on the complexity of real algebraic hypersurfaces,” Graphs and Combinatorics, vol. 27, no. 3, pp. 419–430, 2011.
Kerber M, Sagraloff M. 2011. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 27(3), 419–430.
Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” Graphs and Combinatorics, vol. 27, no. 3, Springer, 2011, pp. 419–30, doi:10.1007/s00373-011-1020-7.

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