Affiliation:
1. 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.
Reference25 articles.
1. Matoušek, J. (2002). Lectures on Discrete Geometry, Springer.
2. Über Affine Geometrie vii: Neue Extremeigenschaften von Ellipse and Ellipsoid;Blaschkle;Leipz. Berichte,1917
3. Un invariante affine para los cuerpos convexos del espacio de n dimensiones;Port. Math.,1943
4. Affine isoperimetric problems;Petty;Ann. N. Y. Acad. Sci.,1985
5. Contributions to affine surface area;Hug;Manuscr. Math.,1996