English

On minimal bases in homotopical combinatorics

Algebraic Topology 2025-06-16 v1 Combinatorics

Abstract

We present a development in the computational suite for the study of NN_\infty operads for a finite group GG. 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 NN_\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.

Keywords

Cite

@article{arxiv.2506.11159,
  title  = {On minimal bases in homotopical combinatorics},
  author = {Katharine Adamyk and Scott Balchin and Miguel Barrero and Steven Scheirer and Noah Wisdom and Valentina Zapata Castro},
  journal= {arXiv preprint arXiv:2506.11159},
  year   = {2025}
}

Comments

42 pages, comments welcome!

R2 v1 2026-07-01T03:14:29.530Z