A real stable extension of the Vamos matroid polynomial

Understand

In 2004, Choe, Oxley, Sokal and Wagner established a tight connection between matroids and multiaffine real stable polynomials.

• Recently, Branden used this theory and a polynomial coming from the Vamos matroid to disprove the generalized Lax conjecture.
• Here we present a 10-element extension of the Vamos matroid and prove that its basis generating polynomial is real stable (i.e.
• that the matroid has the half-plane property).