论文标题
对称组和固定点同质体的作用
Foatic actions of the symmetric group and fixed-point homomesy
论文作者
论文摘要
我们研究了由rényi-foata映射与其他二面体对称性（被认为是0-1矩阵的置换）交织在一起的n置排列的图。迭代这些地图会导致动态系统，在某些情况下，这些系统表现出有趣的轨道结构，例如，每个轨道大小都是两个的力量，以及同源性统计（每个轨道上的平均值相同）。特别是，对于这些图中的三个地图，即使在轨道结构远非良好的情况下，相对于这些图中的三个地图，置换的固定点（aka 1-cycles）的数量似乎是同质的。对于最有趣的“ foatic”动作，我们提供了堆的分析和递归结构，使我们能够证明固定点的同源性和轨道特性，但是另外两种情况仍然是猜想的。
We study maps on the set of permutations of n generated by the Rényi-Foata map intertwined with other dihedral symmetries (of a permutation considered as a 0-1 matrix). Iterating these maps leads to dynamical systems that in some cases exhibit interesting orbit structures, e.g., every orbit size being a power of two, and homomesic statistics (ones which have the same average over each orbit). In particular, the number of fixed points (aka 1-cycles) of a permutation appears to be homomesic with respect to three of these maps, even in one case where the orbit structures are far from nice. For the most interesting such "Foatic" action, we give a heap analysis and recursive structure that allows us to prove the fixed-point homomesy and orbit properties, but two other cases remain conjectural.
