论文标题
有限的免费Motzkin路径及其应用的组合学
Combinatorics on bounded free Motzkin paths and its applications
论文作者
论文摘要
在本文中，我们从一组有界的自由Motzkin路径到一组有界的Motzkin前缀构建了两次培养，该前缀诱导了从一组有界的自由染色器路径到一组有界型戴克前缀的培养。我们还在一组有界无角的Motzkin路径和一组$ t $ core分区和一组有界无角的对称的Motzkin路径和一组自偶联$ t $ core-core分区之间提供了射击。作为一个应用程序，我们获得了具有固定数量拐角数的普通和自轭$ t $ core分区数量的明确公式。
In this paper, we construct a bijection from a set of bounded free Motzkin paths to a set of bounded Motzkin prefixes that induces a bijection from a set of bounded free Dyck paths to a set of bounded Dyck prefixes. We also give bijections between a set of bounded cornerless Motzkin paths and a set of $t$-core partitions, and a set of bounded cornerless symmetric Motzkin paths and a set of self-conjugate $t$-core partitions. As an application, we get explicit formulas for the number of ordinary and self-conjugate $t$-core partitions with a fixed number of corners.
