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Permutation statistics $\wnm$ and $\rlm$ are both arising from permutationtableaux. $\wnm$ was introduced by Chen and Zhou, which was proved equallydistributed with the number of unrestricted rows of a permutation tableau.While $\rlm$ is showed by Nadeau equally distributed with the number of $1$'sin the first row of a permutation tableau.  In this paper, we investigate the joint distribution of $\wnm$ and $\rlm$.Statistic $(\rlm,\wnm,\rlmin,\des,(\underline{321}))$ is shown equallydistributed with $(\rlm,\rlmin,\wnm,\des,(\underline{321}))$ on $S_n$. Then thegenerating function of $(\rlm,\wnm)$ follows. An involution is constructed toexplain the symmetric property of the generating function. Also, we study thetriple statistic $(\wnm,\rlm,\asc)$, which is shown to be equally distributedwith $(\rlmax-1,\rlmin,\asc)$ as studied by Josuat-Verg$\grave{e}$s. The mainmethod we adopt throughout the paper is constructing bijections based on ablock decomposition of permutations.

Block decomposition and statistics arising from permutation tableaux