Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Multinomial probabilities, permanents and a conjecture of Karlin and Rinott

Author: R. B. Bapat
Journal: Proc. Amer. Math. Soc. 102 (1988), 467-472
MSC: Primary 15A15; Secondary 60E15
MathSciNet review: 928962
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The probability density function of a multiparameter multinomial distribution can be expressed in terms of the permanent of a suitable matrix. This fact and certain results on conditionally negative definite matrices are used to prove a conjecture due to Karlin and Rinott.

References [Enhancements On Off] (What's this?)

  • [1] A. D. Alexandroff, Zur theorie der gemischten volumina von konvexen körpern. IV, Mat. Sb. 45 (1938), no. 3, 227-251. (Russian; German summary).
  • [2] G. P. Egorychev, The solution of van der Waerden's problem for permanents, Adv. in Math. 42 (1981), 299-305. MR 642395 (83b:15002b)
  • [3] D. I. Falikman, A proof of van der Waerden's conjecture on the permanent of a doubly stochastic matrix, Mat. Zametki 29 (1981), 931-938. (Russian) MR 625097 (82k:15007)
  • [4] S. Karlin and Y. Rinott, Entropy inequalities for classes of probability distributions. II, The multivariate case, Adv. in Appl. Probab. 13 (1981), 325-351. MR 612207 (84k:60025)
  • [5] M. Marcus and M. Newman, The permanent of a symmetric matrix, Notices Amer. Math. Soc. 8 (1981), 595.
  • [6] C. A. Micchelli, Interpolation of scattered data: Distance matrices and conditionally positive definite matrices, Constr. Approx. 2 (1986), 11-22. MR 891767 (88d:65016)
  • [7] H. Minc, Permanents, Encyclopedia of Mathematics and its Applications, Vol. 6, Addison-Wesley, Reading, Mass., 1978. MR 504978 (80d:15009)
  • [8] K. R. Parthasarathy and K. Schmidt, Positive definite kernels, continuous tensor products and central limit theorems of probability theory, Springer-Verlag, Berlin, 1972. MR 0622034 (58:29849)
  • [9] R. Sinkhorn, A relationship between arbitrary positive matrices and doubly stochastic matrices, Ann. Math. Statist. 35 (1964), 876-879. MR 0161868 (28:5072)
  • [10] J. H. van Lint, Notes on Egoritsjev's proof of the van der Waerden conjecture, Linear Algebra Appl. 39 (1981), 1-8. MR 625232 (82m:15011)
  • [11] D. V. Widder, The Laplace transform, Princeton Univ. Press, Princeton, N.J., 1946.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A15, 60E15

Retrieve articles in all journals with MSC: 15A15, 60E15

Additional Information

Keywords: Permanents, multinomial distribution, conditionally negative definite matrices
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society