Mathematics – Combinatorics
Scientific paper
2011-06-28
Exclusively published in the Electronic Journal <A HREF="http://www.math.rutgers.edu/~zeilberg/pj.html">Personal Journal of
Mathematics
Combinatorics
3 pages
Scientific paper
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 http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/georgy.htm 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 Maple package http://www.math.rutgers.edu/~zeilberg/tokhniot/HISTABRUT">HISTABRUT(in fact, a very tiny part of it, procedure AlphaSeq), explained in this other http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/histabrut.html">neat article, and get a semi-rigorous proof. We also needed the nice little Maple package http://www.math.rutgers.edu/~zeilberg/tokhniot/GuessRat">GuessRat, to do the guessing of rational functions. Equipped with these two packages, Zeilberger wrote a short Maple program http://www.math.rutgers.edu/~zeilberg/tokhniot/SameSexMarriages">SameSexMarriages that enabled the author to generate this paper.
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