I would like to know if there are some interesting partial orders defined on the isomorphism classes of vector bundles on $\mathbb P^n_k$ (you can assume $k$ is $\mathbb C$ if that helps).
Motivation: I am looking at a function which is related to a partial order on vector bundles on the punctured spectrum of a regular local ring. Since the obvious, and much more studied, analogue is vector bundles on $\mathbb P^n_k$, I am curious on what is known in that case. In the case $n=1$, since all vector bundles splits as direct sum of $\mathcal O(a)$, one can obviously use the set of twists to define a partial order. Thanks.