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- W4300426565 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, $0<j<m$, so that the remaining matrix is level. We ask if there is a minimum integer $ell=ell(n,k)$ such that for all $m>ell$, any $mtimes n$ 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 $ngeq 3$ by giving upper and lower bounds for it. We then apply this result to bound the number of certain types of vector space multipartitions." @default.
- W4300426565 created "2022-10-03" @default.
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- W4300426565 date "2014-01-22" @default.
- W4300426565 modified "2023-09-26" @default.
- W4300426565 title "Level Matrices" @default.
- W4300426565 doi "https://doi.org/10.48550/arxiv.1401.5868" @default.
- W4300426565 hasPublicationYear "2014" @default.
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