论文标题
$ K $ - 排序，统计和模式
$k$-arrangements, statistics and patterns
论文作者
论文摘要
$ k $ - 排序是固定点为$ k $颜色的排列。我们证明了与$ k $分组的统计和模式有关的列举结果，证实了Blitvić和Steingrímsson的几个猜想。特别是，他们关于毁灭形式下降数量和$ k $ - 排序的置换形式的猜想之一是通过两种有趣的方式加强的。此外，作为所谓降低值定理的一种应用，我们计算了对称对称的Eulerian统计数据的生成函数，而不是我们的研究中产生的排列。
The $k$-arrangements are permutations whose fixed points are $k$-colored. We prove enumerative results related to statistics and patterns on $k$-arrangements, confirming several conjectures by Blitvić and Steingrímsson. In particular, one of their conjectures regarding the equdistribution of the number of descents over the derangement form and the permutation form of $k$-arrangements is strengthened in two interesting ways. Moreover, as one application of the so-called Decrease Value Theorem, we calculate the generating function for a symmetric pair of Eulerian statistics over permutations arising in our study.
