Sách The toric ideal of a matroid of rank 3 is generated by quadrics

<div>1 Introduction</div><div>The bases of a matroid have many good properties. Combinatorial optimization problems</div><div>among them can be effectively solved. In this paper, we consider the conjecture about the</div><div>bases of a matroid proposed by White [6]. While this conjecture has occasionally been</div><div>stated in terms of algebraic expressions, it is closely related to combinatorial problems.</div><div>Our proof adopts a combinatorial approach.</div><div>A matroid has several equivalent definitions. We define a matroid by a set of subsets</div><div>that satisfies the exchange axiom. A family B of sets is the collection of bases of a matroid</div><div>if it satisfies the exchange axiom given below.</div>