Lexicographic shellability, matroids, and pure order ideals
Lexicographic shellability, matroids, and pure order ideals
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词典可壳性、拟阵和纯序理想
DOI：
10.1016/j.aam.2015.03.003
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
J. A. Samper
中科院分区：
文献类型：
--
作者：
S. Klee;J. A. Samper
1977年Stanley证明了拟阵独立复形的h-向量是纯O-序列。在本文中，我们使用字典序壳拟阵激发一种新的方法来证明斯坦利猜想。这表明可以从脱壳产生的组合数据构建纯O序列。然后，我们证明，我们的猜想持有拟阵的秩最多为4，解决排名4的情况下斯坦利猜想。在一般情况下，我们证明，如果我们的猜想成立的所有rankd拟阵上最多2个元素，那么它成立的所有rankd拟阵。
In 1977 Stanley conjectured that theh-vector of a matroid independence complex is a pureO-sequence. In this paper we use lexicographic shellability for matroids to motivate a new approach to proving Stanley's conjecture. This suggests that a pureO-sequence can be constructed from combinatorial data arising from the shelling. We then prove that our conjecture holds for matroids of rank at most four, settling the rank four case of Stanley's conjecture. In general, we prove that if our conjecture holds for all rankdmatroids on at most 2delements, then it holds for all matroids of rankd.