Abstract:For an integer $c\geq 1$, let $a_c(n)$ count the number of generalized cubic partitions of $n$, which are partitions of $n$ whose even parts may appear in $c$ different colors, and $d_c(n)$ count the number of partitions obtained by adding the links of the $c$-elongated plane partition diamonds of length $n$. We prove in this note infinite families of congruences modulo $7$ and $11$ for $a_c(n)$ and $d_c(n)$ by employing elementary $q$-series techniques. These results generalize particular congruences modulo $7$ and $11$ for $a_c(n)$ and $d_c(n)$ recently found by Dockery, and Baruah, Das, and Talukdar, respectively, using modular forms.
From: Russelle Guadalupe [view email]
[v1]
Tue, 19 Aug 2025 12:41:04 UTC (6 KB)
[v2]
Tue, 16 Dec 2025 16:24:32 UTC (8 KB)
[v3]
Thu, 8 Jan 2026 10:01:20 UTC (9 KB)
[v4]
Thu, 17 Sep 2026 16:52:59 UTC (9 KB)
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