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arXiv · 1401.5868

Level Matrices

George Seelinger·Papa Sissokho·Larry Spence·Charles Vanden Eynden
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Abstract

Let $n>1$ and $k>0$ be fixed integers. A matrix is said to be level if all its column sums are equal. A level matrix with $m$ rows is called reducible if we can delete $j$ rows, $0 \ell$, any $m\times n$ level matrix with entries in $\{0,\ldots,k\}$ is reducible. It is known that $\ell(2,k)=2k-1$. In this paper, we establish the existence of $\ell(n,k)$ for $n\geq 3$ by giving upper and lower bounds for it. We then apply this result to bound the number of certain types of vector space multipartitions.

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George Seelinger, Papa Sissokho, Larry Spence, Charles Vanden Eynden. 2014-01-23. Level Matrices. https://arxiv.org/abs/1401.5868

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