论文标题
Dyck路径，二进制单词和Grassmannian排列避免了增加模式
Dyck paths, binary words, and Grassmannian permutations avoiding an increasing pattern
论文作者
论文摘要
如果最多有一个下降，则置换称为Grassmannian。吉尔（Gil）和托马斯科（Tomasko）在2021年启动了这种排列中模式的研究。我们通过研究避免增加模式的格拉斯曼尼亚排列来继续这项工作。特别是，我们计算了大小$ m $的格拉曼尼亚排列，避免了尺寸$ k $的身份排列，从而解决了韦纳做出的猜想。我们还将我们的计数改进了特殊班级，例如奇怪的格拉斯曼尼亚排列和司芒纳尼亚的互动。我们通过将草个性排列与戴克路径和二进制单词联系起来来证明我们的大部分结果。
A permutation is called Grassmannian if it has at most one descent. The study of pattern avoidance in such permutations was initiated by Gil and Tomasko in 2021. We continue this work by studying Grassmannian permutations that avoid an increasing pattern. In particular, we count the Grassmannian permutations of size $m$ avoiding the identity permutation of size $k$, thus solving a conjecture made by Weiner. We also refine our counts to special classes such as odd Grassmannian permutations and Grassmannian involutions. We prove most of our results by relating Grassmannian permutations to Dyck paths and binary words.
