Quotients in Discrete Convex Analysis

The combinatorial structure of a subspace arrangement can be captured by a polymatroid. The polymatroid arising from the image of the subspace arrangement under a linear map is in an intricate relation with the original polymatroid. This leads to the notion of quotients for submodular functions and M-convex sets.

We lay the foundation for quotients of more general discrete convex functions by giving several equivalent definitions of quotients for M-convex sets. In the talk, I will give a basic introduction to the necessary notions from discrete geometry and matroid theory followed by an overview of new insights.

It is based on joint work with Marie Brandenburg and Ben Smith.