Integrality of hook ratios

Details Integrality of hook ratios Integrality of hook ratios

2011-11-25

arxiv.org/abs/1111.5959v1

Mathematics

Combinatorics

13 pages, 3 figures Keywords: partitions, hook products, Kneser's theorem, McKay numbers, Beurling-Nyman criterion

Scientific paper

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.

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