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- W4364375452 abstract "In the eleventh paper in the series on MacMahon’s partition analysis, Andrews and Paule introduced the [Formula: see text]-elongated partition diamonds. Recently, they revisited the topic. Let [Formula: see text] count the partitions obtained by adding the links of the [Formula: see text]-elongated plane partition diamonds of length [Formula: see text]. Andrews and Paule obtained several generating functions and congruences for [Formula: see text], [Formula: see text], and [Formula: see text]. Da Silva et al. further found many congruences modulo 4, 5, 7, 8, 9, and 11 for [Formula: see text]. In this paper, we extend some individual congruences found by Andrews and Paule and da Silva et al. to their respective families as well as find new families of congruences for [Formula: see text]. We also present a refinement in an existence result for congruences of [Formula: see text] found by da Silva et al. and prove some new individual as well as a few families of congruences modulo 5, 7, 8, 11, 13, 16, 17, 19, 23, 25, 32, 49, 64, and 128." @default.
- W4364375452 created "2023-04-12" @default.
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- W4364375452 date "2023-05-20" @default.
- W4364375452 modified "2023-09-29" @default.
- W4364375452 title "Congruences for k-elongated plane partition diamonds" @default.
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- W4364375452 doi "https://doi.org/10.1142/s1793042123501038" @default.
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