Generalized permutation patterns and a classification of the Mahonian statistics
Generalized permutation patterns and a classification of the Mahonian statistics
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发表时间：
2000
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通讯作者：
E. Babson;E. Steingrímsson
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作者：
E. Babson;E. Steingrímsson
我们引入广义排列模式，我们允许的要求，在一个模式中的两个相邻的字母必须是相邻的排列。我们表明，基本上所有的Mahonian置换统计在文献中可以写为线性组合的这种模式。几乎所有已知的Mahonian排列统计量都可以写成长度不超过3的模式的线性组合。只有十四种可能的Mahonian统计，我们列出。其中，有八个是已知的，我们给另外三个证据。剩下的三个我们推测是Mahonian。我们还给出了一个明确的数值描述的Mahonian统计模式的组合必须有，取决于其模式的最大长度。
We introduce generalized permutation patterns, where we allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We show that essentially all Mahonian permutation statistics in the literature can be written as linear combinations of such patterns. Almost all known Mahonian permutation statistics can be written as linear combinations of patterns of length at most 3. There are only fourteen possible such Mahonian statistics, which we list. Of these, eight are known and we give proofs for another three. The remaining three we conjecture to be Mahonian. We also give an explicit numerical description of the combinations of patterns a Mahonian statistic must have, depending on the maximal length of its patterns.