论文标题
限制增长功能的组合统计数据包含恰好$ K $倍的模式
Combinatorial statistics on restricted growth functions containing a pattern exactly $k$ times
论文作者
论文摘要
在本科论文中，我们扩展了对限制生长功能的统计研究，避免了Campbell等发起的模式。 al。受限的生长功能引起了人们的关注，因为它们与固定分区进行了培养。当受限的增长功能包含恰好$ K $ times的模式时，我们检查了情况，其中$ k = 0 $对应于模式回避。当$ k = 1 $并为这些模式定义一种新型的WILF等效性时，我们证明了几种统计和模式组合的结果。我们还检查了与$ m（n）$，整数分区的poset相关的poset，分为不同的部分，并猜想了新的poset的单程性。我们从该领域的简短历史开始，并以猜想清单结束。
In this undergraduate thesis, we expand on the study of statistics on restricted growth functions avoiding patterns initiated by Campbell, et. al. Restricted growth functions are of interest because they are in bijection with set partitions. We examine the case when a restricted growth function contains a pattern exactly $k$ times, where $k=0$ corresponds to pattern avoidance. We prove results for several statistic and pattern combinations in the case when $k=1$ and define a new type of Wilf equivalence for these patterns. We also examine a poset related to $M(n)$, the poset of integer partitions into distinct parts, and give a conjecture on the new poset's unimodality. We begin with a brief history of the field and end with a list of conjectures.
