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A bijection for Euler’s partition theorem in the spirit of Bressoud

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Abstract

For each positive integer n, we construct a bijection between the odd partitions of n and the distinct partitions of n. Our bijection extends a bijection of Bressoud between the odd-and-distinct partitions of n and the splitting partitions of n. We compare our bijection with the classical bijections of Glaisher and Sylvester, and also with one recently constructed by Chen, Gao, Ji and Li.

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Acknowledgements

Igor Pak told me about the ytableau package for drawing Young diagrams in LaTeX. C. Bessenrodt sent me some useful comments on an earlier draft.

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  1. Department of Mathematics & Statistics, Maynooth University, Co. Kildare, Ireland

    John Murray

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  1. John Murray
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Correspondence to John Murray.

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Murray, J. A bijection for Euler’s partition theorem in the spirit of Bressoud. Ramanujan J 51, 163–175 (2020). https://doi.org/10.1007/s11139-019-00162-z

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  • DOI: https://doi.org/10.1007/s11139-019-00162-z

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