By using the generating tree technique and the obstinate kernel method, Kim and Lin confirmed a conjecture due to Martinez and Savage which asserts that inversion sequences $e=(e_1,e_2,\dots ,e_n)$ containing no three indices $i<j<k$ such that $e_i\ge e_j$, $e_j\ge e_k$ and $e_i>e_k$ are counted by Baxter numbers. In this paper, we provide a bijective proof of this conjecture via an intermediate structure of open partition diagrams, in answer to a problem posed by Beaton-Bouvel-Guerrini-Rinaldi. Moreover, we show that two new classes of pattern-avoiding inversion sequences are also counted by Baxter numbers.

中文翻译：

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避免模​​式反转序列和开放分区图

通过使用生成树技术和顽固核方法，Kim和Lin证实了Martinez和Savage的推测，该推测断言了反演序列 $Ë=（{Ë}_{\mathrm{1个}}，{Ë}_2，\dots ，{Ë}_{ñ}）$ 不包含三个索引 $\mathrm{一世}<Ĵ<ķ$ 这样 ${Ë}_{\mathrm{一世}}\ge {Ë}_{Ĵ}$， ${Ë}_{Ĵ}\ge {Ë}_{ķ}$ 和 ${Ë}_{\mathrm{一世}}>{Ë}_{ķ}$用百特数计算。在本文中，我们通过开放分区图的中间结构提供了这一猜想的双射证明，以应对Beaton-Bouvel-Guerrini-Rinaldi提出的问题。此外，我们表明，通过巴克斯特数也可以计算出两类新的避免模式反转序列。