Results on formally dual sets in finite abelian groups of size 64 obtained from a graph search algorithm

2023/03/27 by Robert Schüler, Schüler, Robert
Mathematics · #20C15 #20K01 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2303.15059

openalex publication_date 2023/03/27 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28

Abstract

We shortly present two small results regarding the study formal duality in finite abelian groups as introduced by Cohn, Kumar, Reiher and Schürmann. In particular, we give a new example of a formally self dual set in ℤ₂²×ℤ₄² and computed nonexistence of primitive formally dual sets of size 8 in ℤ₈².

Related

• Formal Duality in Finite Abelian Groups
• Constructions of Primitive Formally Dual Pairs Having Subsets with Unequal Sizes
• A Direct Construction of Primitive Formally Dual Pairs Having Subsets with Unequal Sizes
• On selected developments in the theory of natural dualities
• Notes on duality theories of abelian groups