Certain eta-quotients and $$\ell $$-regular overpartitions
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DOI: 10.1007/s11139-020-00322-6
Abstract: Let $${\overline{A}}_{\ell }(n)$$ be the number of overpartitions of n into parts not divisible by $$\ell $$ . In this paper, we prove that $${\overline{A}}_{\ell }(n)$$ is almost always divisible by $$p_i^j$$ if $$p_i^{2a_i}\ge \ell… read more here.
Keywords: certain eta; quotients ell; eta quotients; regular overpartitions ... See more keywords
EXTENDING CONGRUENCES FOR OVERPARTITIONS WITH $\ell $ -REGULAR NONOVERLINED PARTS
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DOI: 10.1017/s0004972724001023
Abstract: Abstract Recently, Alanazi et al. [‘Refining overpartitions by properties of nonoverlined parts’, Contrib. Discrete Math. 17(2) (2022), 96–111] considered overpartitions wherein the nonoverlined parts must be $\ell $ -regular, that is, the nonoverlined parts cannot… read more here.
Keywords: regular nonoverlined; overpartitions ell; extending congruences; ell regular ... See more keywords