Abstract
We generalise Euler’s partition theorem involving odd parts and distinct parts for all moduli and provide new companions to Rogers–Ramanujan–Andrews–Gordon identities related to this theorem.
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Acknowledgements
The first author would like to thank Professor Peter Paule and Professor Christian Krattenthaler for their comments on an earlier version of this paper during the Strobl meeting. The authors thank the referee for his comments.
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The first author was supported by the Austria Science Foundation (FWF) Grant SFB F50-06 (Special Research Program “Algorithmic and Enumerative Combinatorics”) and partially supported by the National Natural Science Foundation of China (11101238).
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Xiong, X., Keith, W.J. Euler’s partition theorem for all moduli and new companions to Rogers–Ramanujan–Andrews–Gordon identities. Ramanujan J 49, 555–565 (2019). https://doi.org/10.1007/s11139-018-0103-y
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DOI: https://doi.org/10.1007/s11139-018-0103-y
Keywords
- Euler’s partition theorem
- Rogers–Ramanujan–Andrews–Gordon identities
- Partition identities
- Generating functions
- q-Series