区间序的筛分Enumeration及其它Fishburn结构
Sieved Enumeration of Interval Orders and Other Fishburn Structures
摘要：
根据Eriksen和Sjöstrand（2014）的结果，我们详细介绍了一种从适当的Mahonian结构构建遵循Fishburn分布的结构的技术。这种技术是在Bousquet-Mélou et al.（2010）的bivincular模式上引入的，然后用于引入以前未考虑的一类匹配;明确地，根据右交叉和左嵌套的弧的数量的零对齐匹配。然后，我们定义了Claesson和Linusson（2011）的阶乘偏序集的统计量，计算我们称为错误标记的特征的数量，并证明根据错误标记的数量，阶乘偏序集遵循Fishburn分布。作为我们的方法的结果，我们发现一个身份的菲什伯恩数的Mahonian数。
英文摘要：
Following a result of Eriksen and Sjöstrand (2014) we detail a technique to construct structures following the Fishburn distribution from appropriate Mahonian structures. This technique is introduced on a bivincular pattern of Bousquet-Mélou et al. (2010) and then used to introduce a previously unconsidered class of matchings; explicitly, zero alignment matchings according to the number of arcs which are both right-crossed and left nesting. We then define a statistic on the factorial posets of Claesson and Linusson (2011) counting the number of features which we refer to as mislabelings and demonstrate that according to the number of mislabelings that factorial posets follow the Fishburn distribution. As a consequence of our approach we find an identity for the Fishburn numbers in terms of the Mahonian numbers.
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