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Refinement for sequences in partitions

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Abstract

The k-measure of an integer partition was recently introduced by Andrews, Bhattacharjee, and Dastidar. They established an unexpected nice result, which states that the number of partitions of n with 2-measure m is equal to the number of partitions of n with Durfee square of side m. In this note, we aim to obtain the refinement of their result, which involves two statistics, the smallest part and the length of partitions.

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Acknowledgements

The authors would like to thank the referee for helpful comments and suggestions.

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Authors and Affiliations

  1. School of Science, Jimei University, Xiamen, 361021, People’s Republic of China

    Bernard L. S. Lin & Xiaowei Lin

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  1. Bernard L. S. Lin
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  2. Xiaowei Lin
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Correspondence to Bernard L. S. Lin.

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This work was supported by the National Natural Science Foundation of China (No. 11871246), and the Natural Science Foundation of Fujian Province of China (No. 2019J01328).

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Lin, B.L.S., Lin, X. Refinement for sequences in partitions. Ramanujan J 60, 175–180 (2023). https://doi.org/10.1007/s11139-022-00554-8

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  • DOI: https://doi.org/10.1007/s11139-022-00554-8

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