Geodesic
Arithmetic properties of partition \(k\)-tuples with odd parts distinct
Journal of integer sequences, Tome 19 (2016) no. 5
Let $pod_{-k}(n)$ denote the number of partition $k$-tuples of $n$ wherein odd parts are distinct (and even parts are unrestricted). We establish some interesting infinite families of congruences and internal congruences modulo 4, 16, and 5 for $pod_{-2}(n), pod_{-4}(n)$, and $pod_{-6}(n)$, respectively. We also find Ramanujan-type congruences modulo 5 for $pod_{-3}(n)$ and densities of $pod_{-2}(n), pod_{-3}(n), pod_{-4}(n)$, and $pod_{-6}(n)$ modulo 4, 5, 16, and 5, respectively.
Classification : 05A17, 11P83
Keywords: congruence, partition k-tuple, partition with odd parts distinct 
@article{JIS_2016__19_5_a6,
     author = {Naika,  M.S.Mahadeva and Gireesh,  D.S.},
     title = {Arithmetic properties of partition \(k\)-tuples with odd parts distinct},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {5},
     zbl = {1342.05014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a6/}
}
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Naika,  M.S.Mahadeva; Gireesh,  D.S. Arithmetic properties of partition \(k\)-tuples with odd parts distinct. Journal of integer sequences, Tome 19 (2016) no. 5. http://geodesic.mathdoc.fr/item/JIS_2016__19_5_a6/