Recently, Yan and the first 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 main objective of this paper is to prove two of their conjectures concerning the enumeration of $\underline{12}0$-avoiding inversion or ascent sequences. Additionally, concerning the last entry of $\underline{12}0$-avoiding inversion sequences, we prove two equidistribution results and find a new succession rule for the powered Catalan numbers. Towards a proof of an enumerative conjecture on $\underline{23}14$-avoiding permutations, we offer two refined equidistribution conjectures in connection with 110- and $\underline{12}0$-avoiding inversion sequences.

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的维纳模式，其中三个字母中的两个必须相邻。他们与熟悉的组合家族建立了许多联系，并提出了一些有趣的猜想。本文的主要目的是证明他们的两个关于枚举的猜想。$\underline{12}0$-避免反向或上升序列。另外，关于$\underline{12}0$-避免反演序列，我们证明了两个相等分布的结果，并为幂加泰罗尼亚数找到了新的继承规则。寻求关于的枚举猜想的证明$\underline{23}14$-避免排列，我们提供两个与110-和 $\underline{12}0$-避免反转序列。