Covering the Permutohedron by Affine Hyperplanes

Abstract

An almost cover of a finite set in the affine space is a collection of hyperplanes that together cover all points of the set except one. Using the polynomial method, we determine the minimum size of an almost cover of the vertex set of the permutohedron and address a few related questions.

Conjecture 9 was refuted by Gábor Damásdi