Optimizing periodic point configurations on the plane

Paper Title:

Universally Optimal Periodic Configurations in the Plane

Published on:

28 July 2023

Primary Category:

Classical Analysis and ODEs

Paper Authors:

Doug Hardin,

Nathaniel Tenpas

Bullets

Key Details

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Developed linear programming bounds to optimize periodic point configurations

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Showed a 4-point configuration is optimal among configurations based on the A2 lattice

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Showed a 6-point configuration is optimal among configurations based on the rotated A2 lattice

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Reduced the optimization to a multivariate polynomial interpolation problem

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Proved optimality by constructing interpolants satisfying necessary constraints

Explore the topics in this paper

a2 lattice

lattice patterns

mathematical techniques

optimality proofs

periodic configurations

AI generated summary

Optimizing periodic point configurations on the plane

This paper develops mathematical techniques to find optimal periodic point configurations on the plane. It focuses on configurations made of a small set of points repeated in a lattice pattern. The authors prove optimality results for 4-point and 6-point configurations based on the triangular A2 lattice and its rotations.