Counting compatible indexing systems for Cpn
Michael A. Hill, Jiayun Meng, Nan Li · Orbita Mathematicae · 2023
We count the number of compatible pairs of indexing systems for the cyclic group C p n .Building on work of Balchin, Barnes, and 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.