Block decomposition and statistics arising from permutation tableaux

Permutation statistics wm¯ and rlm are both arising from permutation tableaux. was introduced by Chen Zhou, which proved equally distributed with the number of unrestricted rows a tableau. While is shown Nadeau 1’s in first row In this paper, we investigate joint distribution rlm. Statistic (rlm, wm¯, rlmin, des, (321)) on Sn. Then generating function wm¯) follows. An involution constructed to explain symmetric property function. Also, study triple statistic (wm¯, rlm, asc), be (rlmax−1, asc) as studied Josuat-Vergès. The main method adopt throughout paper constructing bijections based block decomposition permutations.