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{\bf Daniel Goldstein and Richard Stong}
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{\bf On the Number of Possible Row and Column Sums of 0,1-Matrices}
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For $n$ a positive integer, we show that the number of of $2n$-tuples
of integers that are the row and column sums of some $n\times n$
matrix with entries in $\{0,1\}$ is evenly divisible by $n+1$. This
confirms a conjecture of Benton, Snow, and Wallach.
We also consider a $q$-analogue for $m\times n$ matrices. We give an
efficient recursion formula for this analogue. We prove a divisibility
result in this context that implies the $n+1$ divisibility result.
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