论文标题
计数$ c_ {p^n} $的兼容索引系统
Counting compatible indexing systems for $C_{p^n}$
论文作者
论文摘要
我们计算环状组$ c_ {p^n} $的索引系统的兼容对数。在Balchin-Barnes-Roitzheim的基础上，我们表明，这种自然数量是另一个大惊小怪的家族 - -CATALAN数字。我们计算这两种不同的方式：展示兼容性条件如何为可允许的集合数量提供自然的递归公式，并使用列举方式来扩展索引系统，从概念上讲更简单。
We count the number of compatible pairs of indexing systems for the cyclic group $C_{p^n}$. Building on work of Balchin--Barnes--Roitzheim, we show that this sequence of natural numbers is another family of Fuss--Catalan numbers. We count this two different ways: showing how the conditions of compatibility give natural recursive formulas for the number of admissible sets and using an enumeration of ways to extend indexing systems by conceptually simpler pieces.
