An analogue of the Aleksandrov projection theorem for convex lattice polygons
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- by Ning Zhang PDF
- Proc. Amer. Math. Soc. 145 (2017), 2305-2310 Request permission
Abstract:
Let $K$ and $L$ be origin-symmetric convex lattice polytopes in $\mathbb {R}^n$. We study a discrete analogue of the Aleksandrov projection theorem. If for every $u\in \mathbb {Z}^n$, the sets $(K\cap \mathbb {Z}^n)|u^\perp$ and $(L\cap \mathbb {Z}^n)|u^\perp$ have the same number of points, is $K=L$? We give a positive answer to this problem in $\mathbb {Z}^2$ under the additional hypothesis that $(2K\cap \mathbb {Z}^2)|u^\perp$ and $(2L\cap \mathbb {Z}^2)|u^\perp$ have the same number of points for every $u\in \mathbb {Z}^n$.References
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Additional Information
- Ning Zhang
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
- MR Author ID: 1049706
- Email: nzhang2@ualberta.ca
- Received by editor(s): February 17, 2016
- Received by editor(s) in revised form: July 13, 2016
- Published electronically: February 15, 2017
- Additional Notes: The author was partially supported by a grant from NSERC
- Communicated by: Alexander Iosevich
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2305-2310
- MSC (2010): Primary 05B50, 52C05; Secondary 52B20
- DOI: https://doi.org/10.1090/proc/13375
- MathSciNet review: 3626490