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On Integer Solutions to Linear Equations
William George Griffiths
Mathematics Department, School of Arts and Sciences, Southern Polytechnic State University, 1100 South Marietta Parkway, Marietta, GA 30060-2896, USA
solo2987@yahoo.com
Annals of Combinatorics 12 (1) p.53-70 March, 2008
AMS Subject Classification:05
Abstract:
A magic square is an n×n matrix with non-negative integer entries, such that the sum of the entries in each row and column is the same. We study the enumeration and P-recursivity of these in the case in which the sum along each row and column is fixed, with the size n of the matrix as the variable. A method is developed that nicely proves some known results about the case when the row and column sum is 2, and we prove new results for the case when the sum is 3.
Keywords: magic squares, P-recursive, permutation patterns

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