论文标题
反转序列避免模式010
Inversion sequences avoiding the pattern 010
论文作者
论文摘要
反转序列是整数序列$（σ_1，\ dots，σ_n）$，使得$ 0 \ leqslantσ_i<i <i $ for ALL $ 1 \ leqslant i \ leqslant n $。对模式避免反转序列的研究始于2015年和2016年的两篇独立文章和Corteel-Martinez-Savage-weselcouch的两篇独立文章。这两篇初始文章解决了反演序列的枚举，避免了每种图案3的单个模式的枚举。我们通过利用避免模式010的反转序列的分解来解决最终案例。我们的分解需要考虑到最大值，以及在反转序列中发生的不同值的数量。 We then expand our method to solve the enumeration of inversion sequences avoiding the pairs of patterns $\{010, 000\}, \{010, 110\}, \{010, 120\}$, and the Wilf-equivalent pairs $\{010, 201\} \sim \{010, 210\}$.对于考虑了避免模式的反转序列的每个家族，其枚举都需要对某些受约束单词的列举避免使用相同的模式，这也是我们也解决的问题。
Inversion sequences are integer sequences $(σ_1, \dots, σ_n)$ such that $0 \leqslant σ_i < i$ for all $1 \leqslant i \leqslant n$. The study of pattern-avoiding inversion sequences began in two independent articles by Mansour-Shattuck and Corteel-Martinez-Savage-Weselcouch in 2015 and 2016. These two initial articles solved the enumeration of inversion sequences avoiding a single pattern for every pattern of length 3 except the patterns 010 and 100. The case 100 was recently solved by Mansour and Yildirim. We solve the final case by making use of a decomposition of inversion sequences avoiding the pattern 010. Our decomposition needs to take into account the maximal value, and the number of distinct values occurring in the inversion sequence. We then expand our method to solve the enumeration of inversion sequences avoiding the pairs of patterns $\{010, 000\}, \{010, 110\}, \{010, 120\}$, and the Wilf-equivalent pairs $\{010, 201\} \sim \{010, 210\}$. For each family of pattern-avoiding inversion sequences considered, its enumeration requires the enumeration of some family of constrained words avoiding the same patterns, a question which we also solve.
