Geodesic
On the number of possible row and column sums of \(0,1\)-matrices
The electronic journal of combinatorics, Tome 13 (2006)
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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.
DOI : 10.37236/1146
Classification : 05A15, 05B20
Mots-clés : divisibility result 
@article{10_37236_1146,
     author = {Daniel Goldstein and Richard Stong},
     title = {On the number of possible row and column sums of \(0,1\)-matrices},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1146},
     zbl = {1098.05007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1146/}
}
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Daniel Goldstein; Richard Stong. On the number of possible row and column sums of \(0,1\)-matrices. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1146

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