论文标题
反转序列中的质量模式之间的wilf等效性
Wilf equivalences between vincular patterns in inversion sequences
论文作者
论文摘要
反转序列是非阴性整数的有限序列，其中每个条目的值都按其位置从上方界定。在经典情况下，Corteel-Martinez-Savage-weselcouch和Mansour-Shattuck研究了反转序列中的模式，在这种情况下，在任何位置都可以发生模式，并且在连续情况下，Auli-Elizalde只能在此情况下发生，在这种情况下，只有相邻的条目才能形成模式的发生。这些论文根据避免它们的反演序列的数量将长度3的经典和连续模式分类为Wilf等效类。 在本文中，我们考虑了反转序列中的尺度模式，与Babson-Steingr \'ımsson模式相比，在排列中的模式，仅需要某些发生的条件才能相邻，从而概括了经典和连续模式。解决了林和YAN的猜想，我们提供了反转序列中长度3的圆柱模式的完整分类，并将其分为WILF等效类，并分为更限制的类，这些类别考虑了该模式的发生量和此类出现的位置。我们在反转序列中找到了模式的第一个已知实例，其中这两个限制性类别不一致。
Inversion sequences are finite sequences of non-negative integers, where the value of each entry is bounded from above by its position. Patterns in inversion sequences have been studied by Corteel-Martinez-Savage-Weselcouch and Mansour-Shattuck in the classical case, where patterns can occur in any positions, and by Auli-Elizalde in the consecutive case, where only adjacent entries can form an occurrence of a pattern. These papers classify classical and consecutive patterns of length 3 into Wilf equivalence classes according to the number of inversion sequences avoiding them. In this paper we consider vincular patterns in inversion sequences, which, in analogy to Babson-Steingr\'ımsson patterns in permutations, require only certain entries of an occurrence to be adjacent, and thus generalize both classical and consecutive patterns. Solving a conjecture of Lin and Yan, we provide a complete classification of vincular patterns of length 3 in inversion sequences into Wilf equivalence classes, and into more restrictive classes that consider the number of occurrences of the pattern and the positions of such occurrences. We find the first known instance of patterns in inversion sequences where these two more restrictive classes do not coincide.
