对称群与无重性标志h-向量的等价关系
An equivalence relation on the symmetric group and multiplicity-free flag h-vectors
摘要：
本文讨论了对称群S_n上由相邻元素a_i和a_{i+1}（w=a_1.. a_n在S_n中，使得|a_i - a_{i+1}| =1。我们计算等价类的数量和等价类的大小。结果被推广到置换的多重集使用阴影技术。在原问题中，包含单位置换的等价类是某偏序集的线性扩张集。进一步的研究给出了所有有限分次偏序集的特征，其标志h-向量只取值-1，0，1。
英文摘要：
We consider the equivalence relation ~ on the symmetric group S_n generated by the interchange of two adjacent elements a_i and a_{i+1} of w=a_1 ... a_n in S_n such that |a_i - a_{i+1}|=1. We count the number of equivalence classes and the sizes of equivalence classes. The results are generalized to permutations of multisets using umbral techniques. In the original problem, the equivalence class containing the identity permutation is the set of linear extensions of a certain poset. Further investigation yields a characterization of all finite graded posets whose flag h-vector takes on only the values -1, 0, 1.
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