On minimal bases in homotopical combinatorics

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.

42 pages, comments welcome!