论文标题
带有禁止图案的扁平分区集
The sets of flattened partitions with forbidden patterns
论文作者
论文摘要
在排列中，特别是在扁平分区中避免模式的研究是当前研究的活跃领域。在本文中，我们在[n]上估算避免单个模式的不同扁平分区的数量以及两种模式。几个计数序列，即加泰罗尼亚的数字，两个的功率，斐波那契数和motzkin数字。我们还考虑了其他组合统计数据，即运行和倒置，并在统计数据重合的情况下建立一些徒。
The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. In this paper, we count the number of distinct flattened partitions over [n] avoiding a single pattern, as well as a pair of two patterns. Several counting sequences, namely Catalan numbers, powers of two, Fibonacci numbers and Motzkin numbers arise. We also consider other combinatorial statistics, namely runs and inversions, and establish some bijections in situations where the statistics coincide.
