LAUSR

Permutation statistics wm and rlm are both arising from permutation tableaux. wm 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 wm and rlm. Statistic (rlm,wm, rlmin,des, (321)) is shown equally distributed with (rlm, rlmin,wm,des, (321)) on Sn. Then the generating function of (rlm,wm) follows. An involution is constructed to explain the symmetric property of the generating function. Also, we study the triple statistic (wm, 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.