The Minimal Set of Ingleton Inequalities
The Minimal Set of Ingleton Inequalities
The Ingleton inequalities are the inequality constraints known to be required of representable matroids. For a matroid of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> elements, there are 16 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> Ingleton inequalities. In this paper, we show that many of these inequalities are redundant. We explicitly determine the unique minimal set of …