Permutation statistics w$\overline{\text{m}}$ and rlm are both arising from permutation tableaux. w$\overline{\text{m}}$ was introduced by Chen and Zhou, which was proved equally distributed with the number of unrestricted rows of a permutation tableau. While rlm is shown by Nadeau equally distributed with the number of 1’s in the first row of a permutation tableau.

In this paper, we investigate the joint distribution of w$\overline{\text{m}}$ and rlm. Statistic (rlm, w$\overline{\text{m}}$, rlmin, des, (321)) is shown equally distributed with (rlm, rlmin, w$\overline{\text{m}}$, des, (321)) on $S_n$. Then the generating function of (rlm, w$\overline{\text{m}}$) follows. An involution is constructed to explain the symmetric property of the generating function. Also, we study the triple statistic (w$\overline{\text{m}}$, rlm, asc), which is shown to be equally distributed with (rlmax$-$1, rlmin, asc) as studied by Josuat-Vergès. The main method we adopt throughout the paper is constructing bijections based on a block decomposition of permutations.

排列统计 w$\overline{\text{米}}$和 rlm 都来自排列表。瓦$\overline{\text{米}}$由陈和周介绍，证明与排列表的不受限制的行数均匀分布。而 rlm 由 Nadeau 显示，在排列表的第一行中以 1 的数量均匀分布。

在本文中，我们研究了 w 的联合分布$\overline{\text{米}}$和 rlm。统计量 (rlm, w$\overline{\text{米}}$, rlmin, des, ( 321 )) 显示为与 (rlm, rlmin, w$\overline{\text{米}}$, des, ( 321 )) 上${秒}_n$. 那么(rlm, w$\overline{\text{米}}$) 如下。构造一个对合来解释生成函数的对称特性。此外，我们研究了三重统计量 (w$\overline{\text{米}}$, rlm, asc)，这表明与 (rlmax$-$1, rlmin, asc) 由 Josuat-Vergès 研究。我们在整篇论文中采用的主要方法是基于排列的块分解构造双射。