偏序集拟阵的偏序集性质及其应用

The poset properties of poset matroids and some applications

通过对偏序拟阵的偏序集性质和广义拟阵通的偏序集性质的分别研究,得到了偏序集拟阵和广义拟阵二者的关系,即每个偏序集拟阵均为广义拟阵,但反之不然。又利用这种关系得出拟阵中的贪心算法能够推广到偏序集拟阵进而组合格式中,并阐述了利用这种关系对于研究偏序集拟阵理论和广义拟阵理论的一些其他作用。

The relations between poset matroids and greedoids are obtained through dealing with the poset properties of poset matroids and greedoids respectively,i.e.poset matroids are greedoids,but not vice versa.Using the above relations,That the greedy algorithm was getten for matroid can be generalized to poset matroid and further to combinatorial scheme;and at the same time,some other applications are expounded to studying on the poset matroid theory and the greedoid theory.