论文标题
设置分区模式和尺寸索引
Set Partition Patterns and the Dimension Index
论文作者
论文摘要
遏制和回避的概念在设定的分区上提供了自然的部分顺序。萨根（Sagan）和戈特（Goyt）的工作导致了避免套件的回避类别的列举结果，这些套件由达尔伯格（Dahlberg）等人精炼。通过使用组合统计。我们通过计算跨某些分区避免类别的维度指数（由有限组的辐射理论引起的统计量）的分布来继续这项工作。在此过程中，我们获得了非交叉分区和321个避免置换的新联系，以及与许多其他组合对象（例如Motzkin和fibonacci多项式）的连接。
The notion of containment and avoidance provides a natural partial ordering on set partitions. Work of Sagan and of Goyt has led to enumerative results in avoidance classes of set partitions, which were refined by Dahlberg et al. through the use of combinatorial statistics. We continue this work by computing the distribution of the dimension index (a statistic arising from the supercharacter theory of finite groups) across certain avoidance classes of partitions. In doing so we obtain a novel connection between noncrossing partitions and 321-avoiding permutations, as well as connections to many other combinatorial objects such as Motzkin and Fibonacci polynomials.
