# Exact bounds for (λ,n)–stable 0-1 matrices.

Document Type : Research Paper

Author

Faculté de Médecine et des sciences de la santé, Université de Sherbrooke, Sherbrooke, Canada

Abstract

Consider a $v \times v$ $(0,1)$ matrix $A$ with exactly $k$ ones in each row and each column. $A$ is $(\lambda, n)$--stable, if it does not contain any $\lambda \times n$ submatrix with exactly one $0$. If $A$ is $(\lambda, n)$--stable, $\lambda, n \ge 2$, then under suitable conditions on $A$, $v \ge \frac{k}{n} \frac{k(n -1)+(\lambda -2)}{\lambda -2}$. The case of equality leads to new and substantive connections with block designs. The previous bound and characterization of $(\lambda,2)$--stable matrices follows immediately as a special case.

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