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Keywords = discrete Mahler product

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13 pages, 450 KB  
Article
Properties of Convex Lattice Sets under the Discrete Legendre Transform
by Tingting He, Ruifeng Yue and Lin Si
Mathematics 2024, 12(11), 1773; https://doi.org/10.3390/math12111773 - 6 Jun 2024
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Abstract
The discrete Legendre transform is a powerful tool for analyzing the properties of convex lattice sets. In this paper, for t>0, we study a class of convex lattice sets and establish a relationship between vertices of the polar of convex [...] Read more.
The discrete Legendre transform is a powerful tool for analyzing the properties of convex lattice sets. In this paper, for t>0, we study a class of convex lattice sets and establish a relationship between vertices of the polar of convex lattice sets and vertices of the polar of its tdilation. Subsequently, we show that there exists a class of convex lattice sets such that its polar is itself. In addition, we calculate upper and lower bounds for the discrete Mahler product of a class of convex lattice sets. Full article
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