Abstract
In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by them satisfy certain reciprocal relations.
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Acknowledgements
We would like to thank George Andrews and Karl Dilcher for many helpful comments. We also thank the referee for their careful reading and useful suggestions.
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The second author was supported by a Killam Postdoctoral Fellowship from the Killam Trusts.
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Beck, G., Chern, S. Reciprocity between partitions and compositions. Ramanujan J 59, 803–812 (2022). https://doi.org/10.1007/s11139-021-00541-5
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DOI: https://doi.org/10.1007/s11139-021-00541-5