  Consider a partial flag variety $X$ which is not a grassmaninan. Consider
also its cohomology ring ${\rm H}^*(X,\ZZ)$ endowed with the base formed by the
Poincar\'e dual classes of the Schubert varieties. In
\cite{Richmond:recursion}, E. Richmond showed that some coefficient structure
of the product in ${\rm H}^*(X,\ZZ)$ are products of two such coefficients for
smaller flag varieties. Consider now a quiver without oriented cycle. If
$\alpha$ and $\beta$ denote two dimension-vectors, $\alpha\circ\beta$ denotes
the number of $\alpha$-dimensional subrepresentations of a general
$\alpha+\beta$-dimensional representation. In \cite{DW:comb}, H. Derksen and J.
Weyman expressed some numbers $\alpha\circ\beta$ as products of two smaller
such numbers. The aim of this work is to prove two generalisations of the two
above results by the same way.
