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arXiv · 2506.11159

On minimal bases in homotopical combinatorics

Katharine Adamyk·Scott Balchin·Miguel Barrero·Steven Scheirer·Noah Wisdom·Valentina Zapata Castro
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Abstract

We present a development in the computational suite for the study of $N_\infty$ operads for a finite group $G$. This progress is achieved using the simple yet powerful observation that Rubin's generation algorithm can be interpreted as a closure operator. Leveraging this perspective, we establish the existence of minimal bases for $N_\infty$ operads. By investigating these bases for certain families of groups we are led to introduce and analyze several novel combinatorial invariants for finite groups.

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Katharine Adamyk, Scott Balchin, Miguel Barrero, Steven Scheirer, Noah Wisdom, Valentina Zapata Castro. 2025-06-11. On minimal bases in homotopical combinatorics. https://arxiv.org/abs/2506.11159

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