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Arrays with fixed row and column sums. (English) Zbl 0267.05005


MSC:

05A15 Exact enumeration problems, generating functions
05B15 Orthogonal arrays, Latin squares, Room squares
05B30 Other designs, configurations
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References:

[1] Anand, H.; Dumir, V. C.; Gupta, H., A combinatorial distribution problem, Duke Math. J., 33, 757-769 (1966) · Zbl 0144.00401
[2] Grimson, R. C., Some results on the enumeration of symmetric arrays, Duke Math. J., 38, 711-715 (1971) · Zbl 0231.05009
[3] Grimson, R. C., Enumeration of symmetric arrays with different row sums, Rend. Sem. Mat. Univ. Padova, 48 (1972), to appear · Zbl 0276.05014
[4] Gupta, H., On the enumeration of symmetric matrices, Duke Math. J., 38, 709-710 (1971) · Zbl 0225.05010
[5] MacMahon, P. A., Combinatory analysis, Vol. 11 (1916), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · JFM 45.1271.01
[6] Smith, D. A., The number of 4 by 4 magic squares, Notices Am. Math. Soc., 18, 90-91 (1971), Abstract 682-05-1
[7] Stein, M. L.; Stein, P. R., Enumeration of stochastic matrices with integer matrices (1970), Los Alamos Sci. Lab., Univ. of California: Los Alamos Sci. Lab., Univ. of California Los Alamos, N.M
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