A sharp bound for the reconstruction of partitions

Electronic Journal of Combinatorics 15 (2008), #N23, 4 pp.

Answering 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 which lowers this bound to n ≥ k² + 2k and present examples showing that this bound is best possible.

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Note:

Maria Monks, in her paper “The solution to the partition reconstruction problem” independently proved a stronger version of this result.

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