Abstract
As a discrete analogue of Aleksandrov’s projection theorem, it is natural to ask the following question: Can an o-symmetric convex lattice set of the integer lattice Z n be uniquely determined by its lattice projection counts? In 2005, Gardner, Gronchi and Zong discovered a counterexample with cardinality 11 in the plane. In this paper, we will show that it is the only counterexample in Z 2, up to unimodular transformations and with cardinality not larger than 17.
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Zhou, J. On the projections of convex lattice sets. Acta. Math. Sin.-English Ser. 26, 1969–1980 (2010). https://doi.org/10.1007/s10114-010-7164-1
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DOI: https://doi.org/10.1007/s10114-010-7164-1