Algebraic combinatorics of diametric magic circles

R.E. Garcia, M.A. Lane and B.M. Loft

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 82, issue 1, 44-53

Abstract: We provide a definition of a diametric magic circle of order n. In this paper, we use techniques in computational algebraic combinatorics and enumerative geometry to construct and to count d-magic circles. We also provide a description of its minimal Hilbert basis and determine the symmetry operations on d-magic circles. Finally, we give an algorithm for writing a natural d-magic circle in terms of the minimal Hilbert basis.

Keywords: Magic circles; Enumeration; Polyhedral cones; Ehrhart series; Minimal Hilbert basis (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2011:i:1:p:44-53

DOI: 10.1016/j.matcom.2010.09.017

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