2024/02/10 by Tsuyoshi Miezaki, Miezaki, Tsuyoshi, Manabu Oura +5
Mathematics · #05C31 #94B05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Primary 05B35 #Secondary 05C35
paper · pdf · doi:10.48550/arxiv.2402.06845
openalex publication_date 2024/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper [Proceedings of the Japan Academy, Ser. A Mathematical Sciences, 95(10) 111-113], the authors introduce the concept of the Tutte polynomials of genus g and announce that each matroid M can be reconstructed from its Tutte polynomial of genus |B(M)|, where B(M) denotes the family of bases of M. In that paper, we also announced that, for all g, there exist inequivalent matroids that have the same Tutte polynomial of genus g. In this paper, we prove these theorems.