In this paper, we construct a bijection between 3142-avoiding permutations and 3241-avoiding permutations which proves the equidistribution of five classical set-valued statistics. Our bijection also enables us to establish a bijection between 3142-avoiding permutations and 4132-avoiding permutations, and a bijection between 2413-avoiding permutations and 1423-avoiding permutations, both of which preserve five classical set-valued statistics. Our results are generalizations of several conjectures posed by Burstein.

中文翻译：

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长度为 4 的模式的 Wilf 等价性的进一步细化

在本文中，我们构建了3142 避免排列和 3241 避免排列之间的双射，证明了五种经典集值统计的等分布。我们的双射还使我们能够在 3142 避免排列和 4132 避免排列之间建立双射，以及在 2413 避免排列和 1423 避免排列之间建立双射，这两者都保留了五个经典的集值统计量。我们的结果是伯斯坦提出的几个猜想的概括。