论文标题
Burstein的置换猜想，Hong和Li的反转序列猜想和受限的Eulerian分布
Burstein's permutation conjecture, Hong and Li's inversion sequence conjecture, and restricted Eulerian distributions
论文作者
论文摘要
最近，Hong和Li在反转序列中对长度四种模式进行了系统的研究，尤其是，他们推测OEIS条目A218225可以枚举$ 0021 $避免的反转序列的数量。同时，Burtein提出相同的序列还可能计算三组模式限制排列。本文的目的不仅是对Hong和Li的猜想和Bustein的第一个猜想的确认，而且还包括$ \ Mathsf {ides} $统计量在受限的置换案例中涉及的两个更微妙的生成功能身份，以及$ \ MATHSF {ASCF {ASC} $在有限的统计范围内与限制性的反相序列序列相关的统计数据。
Recently, Hong and Li launched a systematic study of length-four pattern avoidance in inversion sequences, and in particular, they conjectured that the number of $0021$-avoiding inversion sequences can be enumerated by the OEIS entry A218225. Meanwhile, Burstein suggested that the same sequence might also count three sets of pattern restricted permutations. The objective of this paper is not only a confirmation of Hong and Li's conjecture and Burstein's first conjecture, but also two more delicate generating function identities with the $\mathsf{ides}$ statistic concerned in the restricted permutation case, and the $\mathsf{asc}$ statistic concerned in the restricted inversion sequence case, which yield a new equidistribution result.
