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

Jack Douthett () and Richard Krantz
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Jack Douthett: University of New Mexico
Richard Krantz: Metropolitan State College

Journal of Combinatorial Optimization, 2007, vol. 14, issue 4, No 1, 385-410

Abstract: Abstract 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.

Keywords: Maximally even; Spectra; Convex weighting functions; Ising model; Musical scales (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-006-9041-5

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