杂耍卡序列
Juggling card sequences
摘要：
杂耍模式可以用一系列卡片来描述，这些卡片记录了每一步中球的相对顺序。这种解释有许多代数和组合性质，与斯特林数，戴克路径，纳拉亚纳数，玻色子正规序，弧标记有向图等有关。其中一些连接进行了调查，特别侧重于枚举杂耍模式满足一定的顺序约束，包括交叉点的数量是固定的。
英文摘要：
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck paths, Narayana numbers, boson normal ordering, arc-labeled digraphs, and more. Some of these connections are investigated with a particular focus on enumerating juggling patterns satisfying certain ordering constraints, including where the number of crossings is fixed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
