Coordinate deletion of zeroes (Q2325751)

Summary: For a family \(A\subseteq\{0,\ldots,k\}^n\), define the \(\delta\)-shadow of \(A\) to be the set obtained from \(A\) by removing from any of its vectors one coordinate that equals zero. Given the size of \(A,\) how should we choose \(A\) to minimise its \(\delta\)-shadow? Our aim in this paper is to show that, for any \(r,\) the family of all sequences with at most \(r\) zeros has minimal \(\delta\)-shadow. We actually give the exact best \(A\) for every size.