%subPlain.tex: a Plain TeX file of a paper by Svante Janson, Blair Seidler, and Doron Zeilberger
%On the Statistics of the Number of Fixed-Dimensional Subcubes in a Random Subset of the n-Dimensional Discrete Unit Cube
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{\bf 
On the Statistics of the Number of Fixed-Dimensional Subcubes in a Random Subset of the n-Dimensional Discrete Unit Cube
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{\it  Svante JANSON, Blair SEIDLER, and Doron ZEILBERGER}
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{\bf Abstract}:  
This paper consists of two indpendent, but related parts.
In the first part we show how how to use symbolic computation to derive
explicit expressions for the first few moments of the number of implicants that a random Boolean function has, or equivalently the number
of fixed-dimensional subcubes contained in a random subset of the ndeimensional cube. These explicit expressions suggest, but do not prove,
that these random variables are always asymptotically normal.
The second part is a full, human-generated proof, of this asymptotic
normality.

{\bf Preface}

{\bf References}


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Svante Janson,
Department of Mathematics, Uppsala University, PO Box 480, SE-751~06 Uppsala, Sweden.
{\tt svante.janson@math.uu.se}


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Blair Seidler and Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt  blair.seidler@math.rutgers.edu} \quad, \quad {\tt DoronZeil@gmail.com}   \quad .


Written: {\bf Feb.  10, 2023}.

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