2025/08/30 by Kariane Calta, Calta, Kariane, Sarah Covey +7
Mathematics · #05B05 (Secondary) #05B25 (Primary) 51E10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2509.00556
openalex publication_date 2025/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two subsets S and T of \mathbbF2n are affinely equivalent if there is an affine automorphism of \mathbbF2n taking S to T. Given a basis of the affine span of S, we can construct a Venn diagram whose regions partition S. We prove that any two bases of aff(S) will have the same Venn diagram up to a linear permutation of the Venn regions. Moreover, we prove that two sets are affinely equivalent if and only if there is a cardinality-preserving linear permutation from the Venn regions of S to the Venn regions of T. We use these results to classify certain Sidon sets up to affine equivalence.