2025/08/28 by Campbell, Rutger, Kim, Donggyu, Jorn van der Pol +1
Mathematics · #05B35 (Primary) 05C35 #05D99 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2508.20843
openalex publication_date 2025/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Dowling geometry Qn(Γ), where Γ is a finite group, is a matroid that generalizes the complete-graphic matroid M(Kn+1). We determine the maximum size of an N-free submatroid of Qn(Γ) for various choices of N, including subgeometries Qm(Γ'), lines U2,ℓ, and graphic matroids M(H). When the group Γ is trivial and N=M(Kt), this problem reduces to Turán's classical result in extremal graph theory. We show that when Γ is nontrivial, a complex dependence on Γ emerges, even when N=M(K4).