On split regular BiHom-Leibniz superalgebras

The goal of this paper is to study the structure of split regular BiHom-Leiniz superalgebras, which is a natural generalization of split regular Hom-Leiniz algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Leiniz superalgebras $\mathfrak{L}$ is of the form $\mathfrak{L}=U+{\sum }_{\text{a}}{I}_{\text{a}}$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_{\text{a}}$, a well described ideal of $\mathfrak{L}$, satisfying $[I_{\text{a}},I_{\text{b}}]=0$ if $[\text{a}]\mathrm{\ne }[\text{b}]$. In the case of $\mathfrak{L}$ being of maximal length, the simplicity of $\mathfrak{L}$ is also characterized in terms of connections of roots.