发表机构
Indian Institute of Science; Indian Institute of Technology, Bombay（印度科学学院; 孟买印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完整分类了长度为三的模式三元组的形状-Wilf-等价类，利用双射编码证明，并枚举了避免这些模式的匹配，扩展了先前结果，发现了与Fuss-Catalan数等序列相关的新组合族。
AI 中文摘要
Ferrers 棋盘上的排列模式避免已成为枚举组合学中的一个核心主题，它与匹配、集合划分及其他组合结构有着重要的联系，因为它允许人们构建 Wilf-等价模式的族。虽然单个模式和长度为三的模式对的形状-Wilf-等价类已被完全确定，但更大模式集的相应分类仍然悬而未决。在本文中，我们提供了长度为三的模式三元组的形状-Wilf-等价类的完整分类。我们的证明使用模式避免横向的雙射编码来建立所有等价类。作为应用，我们枚举了避免长度为三的模式三元组的匹配，除了两个等价类之外的所有情况，扩展了 Bloom 和 Elizalde 的先前结果。这些枚举结果确定了由 Fuss-Catalan 数以及出现在 OEIS 中的其他整数序列计数的额外组合对象族。
英文摘要
Permutation pattern avoidance on Ferrers boards has become a central topic in enumerative combinatorics with important connections to matchings, set partitions, and other combinatorial structures as it allows one to build families of Wilf-equivalent patterns. While shape-Wilf-equivalence classes have been completely determined for individual patterns and pairs of patterns of length three, the corresponding classification for larger pattern sets has remained open. In this paper, we provide a complete classification of the shape-Wilf-equivalence classes of triples of patterns of length three. Our proofs use a bijective encoding of pattern avoiding transversals to establish all equivalence classes. As an application, we enumerate matchings avoiding triples of patterns of length three for all but two equivalence classes, extending previous results of Bloom and Elizalde. These enumerative results identify additional families of combinatorial objects counted by the Fuss-Catalan numbers and by other integer sequences appearing in the OEIS.
