Recently, Yan and the first named author investigated systematically the enumeration of inversion or ascent sequences avoiding vincular patterns of length $3$, where two of the three letters are required to be adjacent. They established many connections with familiar combinatorial families and proposed several interesting conjectures. The objective of this paper is to address two of their conjectures concerning the enumeration of $\underline{12}0$-avoiding inversion or ascent sequences.

中文翻译：

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在 $\underline{12}0$-避免反转和上升序列

最近，Yan 和第一作者系统地研究了倒置或上升序列的枚举，避免了长度为 $3$ 的 vincular 模式，其中三个字母中的两个需要相邻。他们与熟悉的组合族建立了许多联系，并提出了几个有趣的猜想。本文的目的是解决他们关于枚举 $\underline{12}0$-避免反转或上升序列的两个猜想。