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The Perimeter of optimal convex lattice polygons in the sense of different metrics

Published online by Cambridge University Press:  17 April 2009

Miloš Stojaković
Miloš Stojaković
Affiliation:
Institute of Mathematics, Faculty of Science, University of Novi SadTrg D. Obradovića 4, 21000 Novi Sad, Yugoslavia e-mail: [email protected]
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Abstract

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Classes of convex lattice polygons which have minimal lp-perimeter with respect to the number of their vertices are said to be optimal in the sense of the lp-metric.

It is proved that if p and q are arbitrary integers or ∞, the asymptotic expression for the lq-perimeter of these optimal convex lattice polygons Qp(n) as a function of the number of their vertices n is . for arbitrary ɛ > 0, where . and Ap is equal to the area of the planar shape |x|p + |y|p ≤ 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 2 , April 2001 , pp. 229 - 242
Copyright
Copyright © Australian Mathematical Society 2001

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