Abstract
In this chapter, we derive bounds and approximations for the number of M × N matrices with all elements either zero or one and with prespecified row and column sums. We obtain these bounds and approximations by introducing appropriate probability measures on the set of {0,1} M × N matrices, i.e., by constructing a family of random matrices. The technique used here has much wider applicability.
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References
Billingsley, P. Probability and Measure. John Wiley Interscience, New York, 1986.
Block, H. W., Savits, T. H., and Shaked, M. A concept of negative dependence using stochastic ordering. Stat. Prob. Lett. 3, 81–86, 1985.
Efron, B. Increasing properties of Polya frequency functions. Ann. Math. Stat. 36, 272–279, 1965.
Esary, J. D., Proschan, F., and Walkup, D. W. Association of random variables with applications. Ann. Math, Stat. 38, 1967–1974, 1967.
Feller, W. An Introduction to Probability Theory and its Applications, Vol. 2, 2nd ed. John Wiley, New York, 1972.
Shanthikumar, J. G. On stochastic comparison of random vectors. J. Appl. Probab, 24, 123–136, 1987.
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Ott, T.J., Shanthikumar, J.G. (1999). Random Matrices and the Number of {0,1} Matrices with given Row and Column Sums. In: Shanthikumar, J.G., Sumita, U. (eds) Applied Probability and Stochastic Processes. International Series in Operations Research & Management Science, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5191-1_12
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DOI: https://doi.org/10.1007/978-1-4615-5191-1_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7364-3
Online ISBN: 978-1-4615-5191-1
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