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Discrete Mathematics & Theoretical Computer Science |
We study integral ratios of hook products of quotient partitions. This question is motivated by an analogous question in number theory concerning integral factorial ratios. We prove an analogue of a theorem of Landau that already applied in the factorial case. Under the additional condition that the ratio has one more factor on the denominator than the numerator, we provide a complete classification. Ultimately this relies on Kneser's theorem in additive combinatorics.
Source : ScholeXplorer
IsRelatedTo ARXIV 0709.1977 Source : ScholeXplorer IsRelatedTo DOI 10.1112/jlms/jdn078 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0709.1977
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