The Electronic Journal of Combinatorics
Answer in g a question of Cameron, Pretzel and Siemons proved that every integer partition of n >= 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 >= k(2) + 2k and present examples showing that this bound is best possible.
Vatter, Vincent, "A Sharp Bound for the Reconstruction of Partitions" (2008). Open Dartmouth: Faculty Open Access Articles. 2324.