Journal of Combinatorial Optimization

, Volume 14, Issue 4, pp 385–410 | Cite as

Maximally even sets and configurations: common threads in mathematics, physics, and music

  • Jack DouthettEmail author
  • Richard Krantz


Convex (concave) interaction weighting functions are combined with circular configurations of black and white sites to determine configurations that have minimum (maximum) weight. These configurations are called maximally even configurations. It is shown that for a given number of black and white sites, all maximally even configurations are equivalent under rotation and reflection, and a simple algorithm is constructed that generates these configurations. A number of equivalent conditions that determine a maximally even configuration are established. These equivalent conditions permit maximally even configurations to apply to a number of seemingly disparate problems including the dinner table and concentric circles problems, the one-dimensional antiferromagnetic Ising model, and musical scales.


Maximally even Spectra Convex weighting functions Ising model Musical scales 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.University of New MexicoAlbuquerqueUSA
  2. 2.Department of PhysicsMetropolitan State CollegeDenverUSA

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