Some New Congruences for $\mathrm{\ell }$-Regular Multipartitions

For a positive integer $n$, let $B_{{\mathrm{\ell }}_1,\dots ,{\mathrm{\ell }}_r}(n)$ denote the number of $({\mathrm{\ell }}_1,{\mathrm{\ell }}_2,\cdots ,{\mathrm{\ell }}_r)$-regular multipartitions of $n$. If ${\mathrm{\ell }}_1={\mathrm{\ell }}_2=\cdots ={\mathrm{\ell }}_r=\mathrm{\ell }$, then we denote $B_{{\mathrm{\ell }}_1,\dots ,{\mathrm{\ell }}_r}(n)$ as $B_{\mathrm{\ell }}^{(r)}(n)$. In this paper, we prove several infinite families of congruences satisfied by $B_{\mathrm{\ell }}^{(r)}(n)$ for different values of $\mathrm{\ell }$ and $r$.