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Note on the combinatorial formula for nHr

Published online by Cambridge University Press:  09 April 2009

G. Baikunth Nath  and
P. V. Krishna Iyer
G. Baikunth Nath
Affiliation:
Department of Mathematics, University of Queensland, Australia
P. V. Krishna Iyer
Affiliation:
Department of Mathematics, University of Queensland, Australia
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nHr denotes the number of n × n matrices with non-negative integral entries, with row-sums and column-sums all equal to r. Kenji Mano [3] investigated the number nHr in which n distinct objects each replicated r times can be distributed in equal numbers among n cells. He gives an intricate formula for the case r = 2. Recently, Anand et al. [1], making use of partitions, extended it to 3Hr and stated a plausible formula for nHr.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 264 - 268
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Anand, H., Dumir, V. C. and Gupta, H., ‘A Combinatorial Distribution Problem’, Duke Math. J. 33 (1966), 757–769.Google Scholar
[2]David, F. N., and Kendall, M. G., ‘Tables of Symmetric Functions: Part IV’, Biometrika 40 (1953), 427–446.Google Scholar
[3]Mano, Kenji, ‘On the formula of nHr’, Scientific Reports of the Faculty of Literature and Science: Hirosaki University 8 (1961), 58–60.Google Scholar