A Sharp Bound for the Reconstruction of Partitions
A Sharp Bound for the Reconstruction of Partitions
Answering a question of Cameron, Pretzel and Siemons proved that every integer partition of $n\ge 2(k+3)(k+1)$ can be reconstructed from its set of $k$-deletions. We describe a new reconstruction algorithm that lowers this bound to $n\ge k^2+2k$ and present examples showing that this bound is best possible.