98 research outputs found
The Number of Same-Sex Marriages in a Perfectly Bisexual Population is Asymptotically Normal
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.Comment: 3 page
Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux
In how many ways can you place n chocolate pieces all of different sizes in
an n by n chocolate box, in such a way that when you go from left to right and
from top to bottom, there are no gaps AND the sizes increase along each row and
each column? The answer is the well-known OEIS Sequence Number 85. To our
amazement, the analogous sequence for a three-dimensional chocolate box was not
there. Here we fill this gap, and more importantly, offer some computational
and theoretical challenges about enumerating families of Solid Standard Young
Tableaux.Comment: 6 page
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