  In this article we study a special class of vector bundles, called tensors. A
tensor consists of a vector bundle $E$ over a smooth irreducible projective
variety and a morphism of vector bundles $\varphi$. As for classical vector
bundles, there exists a notion of stability for these objects given in terms of
filtrations of the vector bundle $E$. The aim of the present paper is to prove
that if a destabilizing filtration is "too" long then there exists a shorter
subfiltration which destabilizes as well. Moreover, we describe some related
combinatorial problems, which arise from the description of a tensor
$(E,\varphi)$ or, more precisely, a filtration of $E$ as a $a$-dimensional
matrix. Eventually, as example we study semistable tensors on the projective
line.
