Abstract
Recently, Andrews and Chern established a number of congruences modulo 5, 7, 11 and 13 on Beck’s partition statistics NT(r, m, n) and \(M_{\omega }(r,m,n)\), which count the total number of parts in the partitions of n with rank congruent to r modulo m and the total number of ones in the partitions of n with crank congruent to r modulo m, respectively. Motivated by their work, we prove several Andrews–Beck type congruences modulo 2 and 4 for NT(r, m, n) and \(M_{\omega }(r,m,n)\) in this paper.
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Funding
This work was supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX23_3299), the Natural Science Foundation of Jiangsu Province of China (No. BK20221383) and the National Natural Science Foundation of China (No. 11971203).
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This work was supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20221383) and the National Natural Science Foundation of China (Grant 11971203).
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Xuan, Y., Yao, O.X.M. & Zhou, X. Andrews–Beck Type Congruences Modulo 2 and 4 for Beck’s Partition Statistics. Results Math 78, 202 (2023). https://doi.org/10.1007/s00025-023-01980-w
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DOI: https://doi.org/10.1007/s00025-023-01980-w