Some New Congruences for $\ell$-Regular Multipartitions

Srilakshmi Krishnamoorthy; Abinash Sarma

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arXiv · 2311.03248

Some New Congruences for $\ell$-Regular Multipartitions

Srilakshmi Krishnamoorthy·Abinash Sarma

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Abstract

For a positive integer $n$, let $B_{\ell_1,\dots,\ell_r}(n)$ denote the number of $(\ell_1,\ell_2,\cdots,\ell_r)$-regular multipartitions of $n$. If $\ell_1=\ell_2=\cdots=\ell_r=\ell$, then we denote $B_{\ell_1,\dots,\ell_r}(n)$ as $B_\ell^{(r)}(n)$. In this paper, we prove several infinite families of congruences satisfied by $B_\ell^{(r)}(n)$ for different values of $\ell$ and $r$.

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BibTeX RIS

Srilakshmi Krishnamoorthy, Abinash Sarma. 2023-11-06. Some New Congruences for $\ell$-Regular Multipartitions. https://arxiv.org/abs/2311.03248

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