We provide a general recursive method for constructing transfer systems on finite lattices. Using this, we calculate the number of homotopically distinct N∞ operads for dihedral groups Dpⁿ , p > 2 prime, and cyclic groups Cqpⁿ , p ≠ q prime. We then further display some of the beautiful combinatorics obtained by restricting to certain homotopically meaningful N_∞ operads for these groups.
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Balchin et al. (2024) studied this question.
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