@article{Pretzel2005ReconstructionOP,
title={Reconstruction of Partitions},
author={Oliver Pretzel and Johannes Siemons},
journal={Electr. J. Comb.},
year={2005},
volume={11}
}

For the partition x = [x1 ≥ x2 ≥ · · · ≥ xk] of the integer n = ∑ i xi a t-deletion is a partition y = [y1 ≥ y2 ≥ · · · ≥ yk] with xi ≥ yi ≥ 0 and ∑ i (xi−yi) = t. We prove that all partitions of n are reconstructible from their t–deletions if n is sufficiently large in relation to t.