algebraic combinatorics of diametric magic circles

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.