Properties of Convex Lattice Sets under the Discrete Legendre Transform

Tingting He, Ruifeng Yue () and Lin Si ()
Additional contact information
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

Mathematics, 2024, vol. 12, issue 11, 1-13

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.

Keywords: convex lattice sets; polar; discrete Legendre transform; discrete Mahler product (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/11/1773/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/11/1773/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:11:p:1773-:d:1410294

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().