## A polyhedral characterization of border bases

Tomorrow I will give a talk on a recent paper which is joint work with Gábor Braun from the Alfréd Rényi Institute of Mathematics. It deals with the polyhedral characterization of all admissible order ideals (and hence border bases) that exist for a given zero-dimensional ideal. As a hardness result, it also follows that determining an optimal order ideal (w.r.t. to a linear objective function) is NP-hard. This is in particular interesting as it shows that not only computing the L-stable span (the vector space approximation of the ideal) is hard but also choosing a ‘nice’ basis which is a mere basis transformation from a linear algebra point of view (see also my previous post for some more details). Here are the slides:

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