论文标题
关于排列的同质体 - 对FINDSTAT数据库中的地图和统计数据的分析
Homomesies on permutations -- an analysis of maps and statistics in the FindStat database
论文作者
论文摘要
在本文中，我们对置换统计数据和徒图进行了系统的研究，对我们识别并证明同源物现象的122个实例的排列图。当给定映射的每个轨道上的统计量相同时，就会发生同源物。我们研究的地图包括Lehmer代码旋转，相反，补体，FOATA BEDVIEN和KREWERAS补体。研究的统计数据与熟悉的概念（例如反转，下降和排列模式）以及更晦涩的构造有关。除了许多新的同源结果外，我们还讨论了我们的研究方法，在这种方法中，我们使用SageMath搜索FindStat组合统计数据库以识别潜在的同质体。
In this paper, we perform a systematic study of permutation statistics and bijective maps on permutations in which we identify and prove 122 instances of the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on each orbit of a given map. The maps we investigate include the Lehmer code rotation, the reverse, the complement, the Foata bijection, and the Kreweras complement. The statistics studied relate to familiar notions such as inversions, descents, and permutation patterns, and also more obscure constructs. Beside the many new homomesy results, we discuss our research method, in which we used SageMath to search the FindStat combinatorial statistics database to identify potential homomesies.
