Internally Perfect Matroids
Internally Perfect Matroids
复制标题
内完美拟阵
DOI：
10.37236/5746
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Aaron Dall
中科院分区：
文献类型：
--
作者：
Aaron Dall
1977年，Stanley证明了拟阵的$h$-向量是一个$\数学{O}$-序列，并猜想它是一个纯$\数学{O}$-序列。在接下来的几年里，这一猜想的正确性已经被证明适用于各种类型的拟阵，尽管一般情况仍然是开放的。本文利用拉斯维格纳斯的内序引入了一类新的拟阵，我们称之为内完美拟阵。我们证明了这些拟阵满足Stanley猜想，并将它们与已知该猜想成立的其他类拟阵进行了比较。我们还证明了，在一定的删失限制下，内完备有序拟阵的每一个子项都是内完备的。
In 1977 Stanley proved that the $h$-vector of a matroid is an $\mathcal{O}$-sequence and conjectured that it is a pure $\mathcal{O}$-sequence. In the subsequent years the validity of this conjecture has been shown for a variety of classes of matroids, though the general case is still open. In this paper we use Las Vergnas' internal order to introduce a new class of matroids which we call internally perfect. We prove that these matroids satisfy Stanley's Conjecture and compare them to other classes of matroids for which the conjecture is known to hold. We also prove that, up to a certain restriction on deletions, every minor of an internally perfect ordered matroid is internally perfect.