On minimal bases in homotopical combinatorics
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918057378578432 |
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| author | Adamyk, Katharine Balchin, Scott Barrero, Miguel Scheirer, Steven Wisdom, Noah Castro, Valentina Zapata |
| author_facet | Adamyk, Katharine Balchin, Scott Barrero, Miguel Scheirer, Steven Wisdom, Noah Castro, Valentina Zapata |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On minimal bases in homotopical combinatorics Adamyk, Katharine Balchin, Scott Barrero, Miguel Scheirer, Steven Wisdom, Noah Castro, Valentina Zapata Algebraic Topology Combinatorics 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. |
| title | On minimal bases in homotopical combinatorics |
| topic | Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/2506.11159 |