$M$ is an $n\times n$ matrix. Consider the submatrices $M(P;Q)$ formed from $P$ rows and $Q$ columns of $M$ where $P$ and $Q$ are disjoint indices.
Is there some way to encode the various determinants such as $\det M((1,2,4);(3,5,6))$, $\det M((1,2);(3,5))$, and $\det M((1,3);(2,4))$ in a single object much like chromatic polynomials and generating functions.
As a motivation, such determinants represent some kind of information about connections in an adjacency matrix of a graph and connections have information interrelated among each other. Therefore, it feels like the various determinants should be interrelated and that therefore there should be a way to intertwine them all in a single object like chromatic polynomials and generating functions.