By Daniel J. Velleman
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Extra resources for American Mathematical Monthly, volume 117, May 2010
However, because there are at least five cells in the fifth column that contain 4−, an integer must be repeated in that column, which is a contradiction. Incidentally, the same conclusion holds for n ≥ 2 if one allows one of the cells to be empty (hence one column to have only k − 1 distinct integers), and does not permit it to be part of a transversal. In this case, delete a column that does not have the empty cell, and argue as in the preceding proof. 4. THE CASE n ≥ 2k − 1. A moment’s thought shows that it suffices to establish this case when n = 2k − 1.
J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Methuen, London, 1964. 35. W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57 (1970) 97–108. 97 36. D. B. Hitchcock, A history of the Metropolis-Hastings algorithm, Amer. Statist. 57 (2003) 254–257. 1198/0003130032413 37. D. , Approximation Algorithms for NP-Hard Problems, PWS Publishing, Boston, 1997. 38. B. R. Hunt, Bayesian methods in nonlinear digital image restoration, IEEE Trans.
1887186 33. A. Habibi, Two-dimensional Bayesian estimate of images, Proceedings of the IEEE 60 (1972) 878–883. 8787 34. J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Methuen, London, 1964. 35. W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57 (1970) 97–108. 97 36. D. B. Hitchcock, A history of the Metropolis-Hastings algorithm, Amer. Statist. 57 (2003) 254–257. 1198/0003130032413 37. D. , Approximation Algorithms for NP-Hard Problems, PWS Publishing, Boston, 1997.
American Mathematical Monthly, volume 117, May 2010 by Daniel J. Velleman