On minimal bases in homotopical combinatorics

2025/06/11 by Adamyk, Katharine, Balchin, Scott, Barrero, Miguel +3
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.11159

Abstract

We present a development in the computational suite for the study of N_∞ 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_∞ operads. By investigating these bases for certain families of groups we are led to introduce and analyze several novel combinatorial invariants for finite groups.

Citations

• ninfty: A software package for homotopical combinatorics
• Transfer systems for rank two elementary abelian groups: characteristic functions and matchstick games
• Counting compatible indexing systems for C_pⁿ
• Composition closed premodel structures and the Kreweras lattice
• Model structures on finite total orders
• Bi-incomplete Tambara functors
• Self-duality of the lattice of transfer systems via weak factorization\n systems
• Equivariant homotopy commutativity for G=C_pqr
• An Equivariant Tensor Product on Mackey Functors

Related

• The combinatorics of N_∞ operads for C_qpⁿ and D_pⁿ
• Combinatorial homotopy theory for operads
• Counting Generating Invariants Under Semisimple Group and Torus Actions
• Model structures on finite total orders
• Large minimal invariable generating sets in the finite symmetric groups