  In the paper we investigate an algorithmic associative binary operation $*$
on the set $\mathcal{LR}_1$ of Littlewood-Richardson tableaux with entries
equal to one. We extend $*$ to an algorithmic nonassociative binary operation
on the set $\mathcal{LR}_1\times \mathbb{N}$ and show that it is equivalent to
the operation of taking the generic extensions of objects in the category of
homomorphisms from semisimple nilpotent linear operators to nilpotent linear
operators. Thus we get a combinatorial algorithm computing generic extensions
in this category.
