Taiwanese Journal of Mathematics

ON THE MINIMUM AREA OF CONVEX LATTICE POLYGONS

Tian-Xin Cai

Full-text: Open access

Abstract

A convex polygon is a polygon whose vertices are points on the integer lattice with interior angles all convex. Let $a(v)$ be the least possible area of a convex lattice polygon with $v$ vertices. It is known that $cv^{2.5}\leq a(v)\leq (15/784)v^3 + o(v^3)$. In this paper, we prove that $a(v)\geq (1/1152)v^3 + O(v^2)$.

Article information

Source
Taiwanese J. Math., Volume 1, Number 4 (1997), 351-354.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406114

Digital Object Identifier
doi:10.11650/twjm/1500406114

Mathematical Reviews number (MathSciNet)
MR1486557

Zentralblatt MATH identifier
0897.52002

Subjects
Primary: 11H06: Lattices and convex bodies [See also 11P21, 52C05, 52C07] 52C05: Lattices and convex bodies in $2$ dimensions [See also 11H06, 11H31, 11P21]

Keywords
convex lattice polygons minimum area admissible n-sequence

Citation

Cai, Tian-Xin. ON THE MINIMUM AREA OF CONVEX LATTICE POLYGONS. Taiwanese J. Math. 1 (1997), no. 4, 351--354. doi:10.11650/twjm/1500406114. https://projecteuclid.org/euclid.twjm/1500406114


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