Some results on the avoidance of vincular patterns by multisets
Some results on the avoidance of vincular patterns by multisets
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DOI：
10.1016/j.dam.2014.10.011
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
T. Mansour;M. Shattuck
中科院分区：
文献类型：
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作者：
T. Mansour;M. Shattuck
单行或虚线模式类似于经典模式，只不过出现中的某些字母必须满足邻接要求。在本文中，我们展示了一些关于通过多集排列避免 vinulous 模式的一般等价性。我们通过定义保留每个字母出现次数的各种回避类之间的双射来证明我们的结果。因此，我们获得了多集排列的 (2, 1, 1) 类型模式的完整 Wilf 分类，当采用数字证据时，这也产生了组合和 k 元词的完整分类。
Vincular or dashed patterns resemble classical patterns except that some of the letters within an occurrence must satisfy an adjacency requirement. In this paper, we show some general equivalences concerning the avoidance of vincular patterns by multiset permutations. We prove our results by defining bijections between various avoidance classes that preserve the number of occurrences of each letter. As a consequence, we obtain for multiset permutations the complete Wilf-classification of patterns of type (2, 1, 1), which also yields the complete classification for compositions and k-ary words when taken with numerical evidence.