Dehaye, Paul-Olivier - Integrality of hook ratios

dmtcs:3022 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Integrality of hook ratios

Authors: Dehaye, Paul-Olivier

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: Kneser's theorem, McKay numbers, Beurling-Nyman criterion,partitions, hook products,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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