By Shalosh B. EKHAD
(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)
Written: April 27, 2011.
Why bother with fully rigorous proofs when one can very quickly get semi-rigorous ones? Yes, yes, we know how to get a "rigorous" proof of the result stated in the title of this article. One way is the boring, human one, citing some heavy guns of theorems that already exist in the literature. We also know how to get a fully rigorous proof automatically, using the methods in this neat article (but it would be a little more complicated, since the probability generating polynomial is not "closed form" but satisfies a second-order recurrence gotten from the Zeilberger algorithm), otherwise the same method would work, alas, it is not yet implemented.
Instead, we chose to use the great package HISTABRUT (in fact, a very tiny part of it, procedure AlphaSeq), explained in this other neat article, and get a semi-rigorous proof. We also needed the nice little Maple package GuessRat, to do the guessing of rational functions.
Equipped with these two packages, Zeilberger wrote a short Maple program SameSexMarriages that enabled the author to generate this paper.
Here is input file that generated the output file .
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