A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al. in 2015. In a recent paper Kitaev and Zhang examined the distribution of the aforementioned patterns. The aim of this paper is to prove more equidistributions of mesh pattern and confirm Kitaev and Zhang's four conjectures by constructing two involutions on permutations.

中文翻译：

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长度为2的网格模式的均等分布以及Kitaev和Zhang的猜想

Hilmarsson等人进行了避免长度为2的网格模式的系统研究。2015年，Kitaev和Zhang在最近的一篇论文中研究了上述模式的分布。本文的目的是通过构造置换的两次对合来证明网格模式的更多均匀分布，并确认Kitaev和Zhang的四个猜想。