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arXiv · 2312.01883

Density results for the parity of $(4k,k)$-singular overpartitions

Victor Manuel Aricheta·Jerome Dimabayao·Hazel Joy Shi
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Abstract

The $(k,i)$-singular overpartitions, combinatorial objects introduced by Andrews in 2015, are known to satisfy Ramanujan-type congruences modulo any power of prime coprime to $6k$. In this paper we consider the parity of the number $\overline{C}_{k,i}(n)$ of $(k,i)$-singular overpartitions of $n$. In particular, we give a sufficient condition on even values of $k$ so that the values of $\overline{C}_{4k,k}(n)$ are almost always even. Furthermore, we show that for odd values of $k \leq 23$, $k\neq 19$, certain subsequences of $\overline{C}_{4k,k}(n)$ are almost always even.

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Victor Manuel Aricheta, Jerome Dimabayao, Hazel Joy Shi. 2023-12-04. Density results for the parity of $(4k,k)$-singular overpartitions. https://arxiv.org/abs/2312.01883

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