Pattern avoidance in biwords
Pattern avoidance in biwords
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双词中的模式避免
DOI：
10.1016/j.disc.2021.112635
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发表时间：
2022
影响因子：
0.8
通讯作者：
Suijie Wang
中科院分区：
文献类型：
--
作者：
Zhijun Cai;Jian Ding;Zhousheng Mei;Suijie Wang
本文研究了每个块中没有重复的双字集合上的模式回避问题，证明了避开π∈ S3的双字的数量与π∈ S3的选择无关，这推广了克努特关于避开π∈ S3的排列的经典结果。我们提出了双射和归纳的方法证明。作为应用，我们将通过双字的模式避免给出Catalan，Riordan和Motzkin数的新的组合解释。利用对称函数的初等理论，我们研究了双字的生成函数，避免了几种特定的模式。
In this paper, we study pattern avoidance on the set of biwords with no repetitions in each block and prove that the number of those biwords avoiding π‾ is independent of the choice of π∈ S 3, which extends Knuth's classic result on permutations avoiding π∈ S 3. We present the proof in both bijective and inductive methods. As applications, we will give new combinatorial interpretations on Catalan, Riordan, and Motzkin numbers via pattern avoidance of biwords. Using the elementary theory of symmetric functions, we investigate the generating functions of biwords avoiding several specific patterns.