Abstract
We give an alternative construction for a family of partition generating functions due to Kanade and Russell. In our alternative construction, we use ordinary partitions instead of jagged partitions. We also present new generating functions which are evidently positive series for partitions due to Kanade and Russell. To obtain those generating functions, we first construct an evidently positive series for a key infinite product. In that construction, a series of combinatorial moves is used to decompose an arbitrary partition into a base partition together with some auxiliary partitions that bijectively record the moves.
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Acknowledgements
The majority of the results in this paper are from the second author’s Ph.D. dissertation. The first author acknowledges Bilim Akademisi BAGEP support with gratitute. The authors thank the referees for the constructive comments, recommendations, and for pointing out the reference [1]; which definitely helped to improve the readability of the paper.
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Communicated by Sylvie Corteel.
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Kurşungöz, K., Ömrüuzun Seyrek, H. Construction of Evidently Positive Series and an Alternative Construction for A Family of Partition Generating Functions Due to Kanade and Russell. Ann. Comb. 26, 903–942 (2022). https://doi.org/10.1007/s00026-022-00597-0
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DOI: https://doi.org/10.1007/s00026-022-00597-0