On computational complexity of plane curve invariants
The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusion of topology, combinatorics, and analysis. The theory remains fairly undeveloped. We review existing methods to describe generic smooth closed plane curves combinatorially, introduce a new one, and giv...
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sg-ntu-dr.10356-1071882023-02-28T19:35:04Z On computational complexity of plane curve invariants Tao, Biaoshuai Duzhin, Fedor School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Analysis The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusion of topology, combinatorics, and analysis. The theory remains fairly undeveloped. We review existing methods to describe generic smooth closed plane curves combinatorially, introduce a new one, and give an algorithm for efficient computation of Arnold's invariants. Our results provide a good source of future research projects that involve computer experiments with plane curves. The reader is not required to have background in topology and even undergraduate students with basic knowledge of differential geometry and graph theory will easily understand our paper. Published version 2015-04-13T09:09:25Z 2019-12-06T22:26:16Z 2015-04-13T09:09:25Z 2019-12-06T22:26:16Z 2014 2014 Journal Article Duzhin, F., & Tao, B. (2014). On computational complexity of plane curve invariants. Online journal of analytic combinatorics, 9. 1931-3365 https://hdl.handle.net/10356/107188 http://hdl.handle.net/10220/25396 http://analytic-combinatorics.org/index.php/ojac/article/view/P2 en Online journal of analytic combinatorics This work is licensed under a Creative Commons Attribution 3.0 License. 11 p. application/pdf |
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DRNTU::Science::Mathematics::Analysis Tao, Biaoshuai Duzhin, Fedor On computational complexity of plane curve invariants |
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The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusion of topology, combinatorics, and analysis. The theory remains fairly undeveloped. We review existing methods to describe generic smooth closed plane curves combinatorially, introduce a new one, and give an algorithm for efficient computation of Arnold's invariants. Our results provide a good source of future research projects that involve computer experiments with plane curves. The reader is not required to have background in topology and even undergraduate students with basic knowledge of differential geometry and graph theory will easily understand our paper. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Tao, Biaoshuai Duzhin, Fedor |
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Article |
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Tao, Biaoshuai Duzhin, Fedor |
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Tao, Biaoshuai |
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On computational complexity of plane curve invariants |
title_short |
On computational complexity of plane curve invariants |
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On computational complexity of plane curve invariants |
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On computational complexity of plane curve invariants |
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On computational complexity of plane curve invariants |
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on computational complexity of plane curve invariants |
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2015 |
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https://hdl.handle.net/10356/107188 http://hdl.handle.net/10220/25396 http://analytic-combinatorics.org/index.php/ojac/article/view/P2 |
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