Arithmetic properties for 7-regular partition triples

Shane Chern (), Dazhao Tang () and Ernest X. W. Xia ()
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Shane Chern: The Pennsylvania State University
Dazhao Tang: Chongqing University
Ernest X. W. Xia: Jiangsu University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 717-733

Abstract: Abstract Let Tℓ(n) denote the number of ℓ-regular partition triples of n. In this paper, we consider the arithmetic properties of T7(n). An infinite family of congruences modulo powers of 7 and several congruences modulo 7 are established. For instance, we prove that for all n ≥ 0 and α ≥ 1, $${T_7}\left( {{7^{2\alpha }}n + \frac{{3 \times {7^{2\alpha }} - 3}}{4}} \right) \equiv 0\;(\bmod {7^\alpha })$$

Keywords: Partitions; arithmetic properties; ℓ-regular partition triples; 05A17; 11P83 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-020-0426-4

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