The classification of Leibniz superalgebras of nilindex n+m (m eq 0)

In this paper we investigate the description of the complex Leibniz superalgebras with nilindex n+m, where n and m ($m eq 0$) are dimensions of even and odd parts, respectively. In fact, such superalgebras with characteristic sequence equal to $(n_1, ..., n_k | m_1, ..., m_s)$ (where $n_1+... +n_k=n, m_1+ ... + m_s=m$) for $n_1geq n-1$ and $(n_1, ..., n_k | m)$ were classified in works cite{FilSup}--cite{C-G-O-Kh1}. Here we prove that in the case of $(n_1, ..., n_k| m_1, ..., m_s)$, where $n_1leq n-2$ and $m_1 leq m-1$ the Leibniz superalgebras have nilindex less than n+m. Thus, we complete the classification of Leibniz superalgebras with nilindex n+m.