The solution to the partition reconstruction problem |
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Authors: | Maria Monks |
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Institution: | 290 Massachusetts Avenue, Cambridge, MA 02139, United States |
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Abstract: | Given a partition λ of n, a k-minor of λ is a partition of n−k whose Young diagram fits inside that of λ. We find an explicit function g(n) such that any partition of n can be reconstructed from its set of k-minors if and only if k?g(n). In particular, partitions of n?k2+2k are uniquely determined by their sets of k-minors. This result completely solves the partition reconstruction problem and also a special case of the character reconstruction problem for finite groups. |
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Keywords: | Partitions Reconstruction problems |
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