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The combinatorics of $N_\infty$ operads for $C_{qp^n}$ and $D_{p^n}$
Scott Balchin, Ethan MacBrough, Kyle Ormsby
Journal:

Glasgow Mathematical Journal , First View

Published online by Cambridge University Press:

03 October 2024, pp. 1-17
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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 $D_{p^n}$, $p \gt 2$ 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.