Original article: Algebraic combinatorics of diametric magic circles

  • Authors:

  • R. E. Garcia;M. A. Lane;B. M. Loft

  • Affiliations:

  • Sam Houston State University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, United States;Sam Houston State University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, United States;Sam Houston State University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, United States

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2011

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Abstract

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.