Karpenkov, Oleg ORCID: 0000-0002-3358-6998
(2006)
Elementary notions of lattice trigonometry.
2008. The
second part in Funct. Anal. Other Math., 2 (2).
pp. 2-4.
Text
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Abstract
In this paper we study properties of lattice trigonometric functions of lattice angles in lattice geometry. We introduce the definition of sums of lattice angles and establish a necessary and sufficient condition for three angles to be the angles of some lattice triangle in terms of lattice tangents. This condition is a version of the Euclidean condition: three angles are the angles of some triangle iff their sum equals \pi. Further we find the necessary and sufficient condition for an ordered n-tuple of angles to be the angles of some convex lattice polygon. In conclusion we show applications to theory of complex projective toric varieties, and a list of unsolved problems and questions.
Item Type: | Article |
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Additional Information: | 49 pages; 16 figures |
Uncontrolled Keywords: | math.CO, math.CO, math.NT, 11H06, 52B20 |
Depositing User: | Symplectic Admin |
Date Deposited: | 09 May 2016 10:05 |
Last Modified: | 19 Jan 2023 07:37 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3001123 |