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Enumerating Solutions of a System of Linear Inequalities Related to Magic Squares
Mikl¨Žs B¨Žna1 and Hyeong-Kwan Ju2
1Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
bona@math.ufl.edu
2Department of Mathematics, Chonnam National University, Kwangju 500-757, Korea
hkju@chonnam.ac.kr
Annals of Combinatorics 10 (2) p. 179-191 June, 2006
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. B¨Žna, 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.