Mathematical Sciences: Growth Rates of Minor-closed Classes of Matroids

这个项目集中在拟阵理论中的两个问题。 第一个是证明了小闭的大小函数 类拟阵要么是无限的，指数的，或 多项式 第二个问题是， 次闭类C被线性函数有界当且仅当 如果有一个有限的上限的临界指数 拟阵C. 拟阵理论是图论的自然推广 和射影几何，因此占据了一个中心位置， 组合理论

This project focusses on two problems in matroid theory. The first is to show that the size functions of minor-closed classes of matroids are either infinite, exponential, or polynomial. The second is to show that the size function of a minor-closed class C is bounded by a linear function if and only if there is a finite upper bound on the critical exponent of matroids in C. Matroid theory is a natural generalization of graph theory and projective geometry, and thus ocupies a central place in combinatorial theory.