Counting compatible indexing systems for C_pⁿ

2022/12/21 by Michael A. Hill, Hill, Michael A., Jiayun Meng +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2212.11250

openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We count the number of compatible pairs of indexing systems for the cyclic group C_pⁿ. 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.

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