A comparison of two methods for random labellings of balls by vectors of integers

(Appeared in Advances in Combinatorial Methods and Applications to Probability and Statistics, N. Balakrishnan, ed., Birkhauser, 1997, [Mohanty Festschrift].)

Sometimes it is worth it, being married to a scientist. In 1982, I wrote a paper with Jane's postdoc advisor, about T.L. Hill's method for solving linear equations, using trees. One Sunday, in Nov. 94, Jane, our youngest daughter Hadas, and I went, as we sometimes do, to Jeff's Bagels coffee bar, near Princeton, and who do we bump to, Greg Kirk, who was a friend and colleague of Jane from her second postdoc, at Princeton, back in 1983. Meanwhile he became a department head in a bio-technology company. After five minutes of gossiping, he told me about this fascinating problem, that came up in the field. He was hoping that the second method was much better. I had to tell him that it was only a little better, as the present paper shows. Jane and Barbara (Greg's wife) liked the paper, since Greg, as a token payment for my `consulting' took us out to a fancy restaurant, that a poor professor like myself cannot usually afford.

This paper is dedicated to Sri Gopal Mohanty, one of the greatest minds in the border-line between combinatorics and statistics.

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