Rota猜想（即对任意的有限域F，F不可表示的最小拟阵个数是有限的。）由Rota在1970年国际数学大会上提出，是拟阵中最基本也是最核心的一个问题，它的解决将对拟阵结构及算法的研究起很大的推动作用。本课题主要研究如下问题：（1）当n取足够大时，如果一个round拟阵M含PG(n-1,q)子式但不含U_{2,q^2+1}子式，则M是否一定不含U_{2,q+2}子式？（2）设M为任意有限域的一个excluded minor，经过任意多次的cosegment-segment 变换后得到的拟阵最多有一个多大的U_{2,n}子式？（3）含 k*k grid子式但不含PG(n-1,q)子式的拟阵有什么结构？这些问题的解决及解决这些问题中用到的思路和技巧将在很大程度上促进Rota猜想的解决。

Rota's Conjecture that the number of excluded minors over a finite field is finite proposed by Rota on the Proceedings of International Congress of Mathematics in 1970 is a very fundamental and important question in matroid theory, whose solution would greatly impulse the study of matroid structure and alogrithm. We will mainly consider the following questions in this project. (1) Let M be a round matroid with a PG(n-1,q)-minor but no U_{2,q^2+1}-minor. Whether does M contain a U_{2,q+2}-minor when n is sufficiently large? (2) Let M be an excluded minor over a finite field. Whether does M contain a large line after a sequence of cosegment-segment exchanges? (3) What is the structure of matroids with k*k grid-minor but no PG(n-1,q)-minor？These qustions'solution and the ideas and teniques used to solve these questions would be of great use to Rota's Conjecture.