Quasi-filiform Leibniz algebras of maximum length

The $n$-dimensional $p$-filiform Leibniz algebras of maximum length have already been studied with $0\le p\le2$. For Lie algebras whose nilindex is equal to $n-2$ there is only one characteristic sequence, $(n-2,1,1)$, while in Leibniz theory we obtain the two possibilities: $(n-2,1,1)$ and $(n-2,2)$. The first case (the $2$-filiform case) is already known. The present paper deals with the second case, i.e., quasi-filiform non-Lie-Leibniz algebras of maximum length. Therefore this work completes the study of the maximum length of the Leibniz algebras with nilindex $n-p$ with $0\le p\le2$.