The combinatorics of N∞ operads for Cqpn and Dpn

Scott Balchin; Ethan MacBrough; Kyle Ormsby

The combinatorics of N∞ operads for Cqpn and Dpn

Scott Balchin, Ethan MacBrough, Kyle Ormsby

School of Mathematics and Physics

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Abstract

We provide a general recursive method for constructing transfer systems on finite lattices. Using this we calculate the number of homotopically distinct $N_\infty$ operads for dihedral groups $D_{p^n}$, $p > 2$ prime, and cyclic groups $C_{qp^n}$, $p \neq q$ prime. We then further display some of the beautiful combinatorics obtained by restricting to certain homotopically meaningful $N_\infty$ operads for these groups.

Original language	English
Number of pages	17
Journal	Glasgow Mathematical Journal
Early online date	03 Oct 2024
Publication status	Early online date - 03 Oct 2024

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The combinatorics of $N_\infty$ operads for $C_{qp^n}$ and $D_{p^n}$
Copyright 2024 the authors. This is an accepted manuscript distributed under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
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AB - We provide a general recursive method for constructing transfer systems on finite lattices. Using this we calculate the number of homotopically distinct $N_\infty$ operads for dihedral groups $D_{p^n}$, $p > 2$ prime, and cyclic groups $C_{qp^n}$, $p \neq q$ prime. We then further display some of the beautiful combinatorics obtained by restricting to certain homotopically meaningful $N_\infty$ operads for these groups.

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The combinatorics of N∞ operads for Cqpn and Dpn

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