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Properties of Convex Lattice Sets under the Discrete Legendre Transform

Author

Listed:
  • Tingting He

    (College of Science, Beijing Forestry University, Beijing 100083, China)

  • Ruifeng Yue

    (College of Science, Beijing Forestry University, Beijing 100083, China)

  • Lin Si

    (College of Science, Beijing Forestry University, Beijing 100083, China)

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 lattice sets and vertices of the polar of its t − dilation. 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.

Suggested Citation

  • Tingting He & Ruifeng Yue & Lin Si, 2024. "Properties of Convex Lattice Sets under the Discrete Legendre Transform," Mathematics, MDPI, vol. 12(11), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1773-:d:1410294
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    References listed on IDEAS

    as
    1. Leonid V. Bogachev & Sakhavet M. Zarbaliev, 2023. "Inverse Limit Shape Problem for Multiplicative Ensembles of Convex Lattice Polygonal Lines," Mathematics, MDPI, vol. 11(2), pages 1-23, January.
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