偏序集拟阵与广义拟阵的关系

Relations between poset matroids and greedoids

研究了偏序集拟阵与广义拟阵的关系.利用偏序集拟阵秩闭包算子的性质与广义拟阵闭包算子性质的比较得出:偏序集拟阵为广义拟阵;通过广义拟阵自同构群的公理系统与偏序集拟阵相应性质的比较得出:广义拟阵不一定为偏序集拟阵.

This paper deals with the relations between poset matroids and greedoids. The first is to show that any poset matroid is a greedoid by comparing the property of rank closure operator of poset matroids with the relative property of closure operator of greedoids. In addition, by comparing the axioms of automorphism group of greedoids with that of poset matroids, it is proved that a greedoid is not necessary a poset matroid.