2023/03/09 by Tong Jin, Jin, Tong, Donggyu Kim +1 · 2 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2303.05353
openalex publication_date 2023/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We generalize Baker-Bowler's theory of matroids over tracts to orthogonal matroids, define orthogonal matroids with coefficients in tracts in terms of Wick functions, orthogonal signatures, circuit sets, and orthogonal vector sets, and establish basic properties on functoriality, duality, and minors. Our cryptomorphic definitions of orthogonal matroids over tracts provide proofs of several representation theorems for orthogonal matroids. In particular, we give a new proof that an orthogonal matroid is regular if and only if it is representable over \mathbbF2 and \mathbbF3, which was originally shown by Geelen, and we prove that an orthogonal matroid is representable over the sixth-root-of-unity partial field if and only if it is representable over \mathbbF3 and \mathbbF4.