If two partitions are conjugate, their multisets of hook lengths are the same. Then one may wonder whether the multiset of hook lengths of a partition determines a partition up to conjugation. The answer turns out to be no. However, we may add an extra condition under which a given multiset of hook lengths determines a partition uniquely up to conjugation. Herman-Chung, and later Morotti found such a condition. We give an alternative proof of Morotti's theorem and generalize it.
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics