Annals of Combinatorics 10 (2006) 179-191Enumerating Solutions of a System of Linear Inequalities Related to Magic Squares Miklós Bóna and Hyeong-Kwan Ju Department of Mathematics, University of Florida, Gainesville, FL 32611, USA Department of Mathematics, Chonnam National University, Kwangju 500-757, Korea Received March 1, 2005 AMS Subject Classification: 05A15, 05B15 Abstract. We enumerate the solutions of a system of a simple homogeneous linear inequalities, motivated by magic squares and their generalizations. We also compute the generating function of these numbers, and prove that it is a rational function. Keywords: rational generating functions, transfer-matrix Method, quasi-polynomial, difference operator References 1. M. Bóna, A Walk Through Combinatorics, World Scientific, New Jersey, 2002. 2. H.-K. Ju, Counting of (n; n)-bipartite graph of degree of at most two, preprint. 3. P.A. MacMahon, Combinatorial Analysis, Vols. 1-2, Cambridge University Press, 1916. 4. R. Stanley, Combinatorics and Commutative Algebra, Birkhäuser, Boston, 1983. 5. R. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge University Press, Cambridge, 1999. 6. H. Wilf, Generatingfunctionology, Academic Press, San Diego, 1994. |