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

Combinatorial algorithms for binary operations on LR-tableaux with entries equal to 1 with applications to nilpotent linear operators