Geodesic
Orthogonal matroids over tracts
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e130

Voir la notice de l'article provenant de la source Cambridge University Press

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 ${\mathbb F}_2$ and ${\mathbb F}_3$, which was originally shown by Geelen [16], 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 ${\mathbb F}_3$ and ${\mathbb F}_4$. 
Jin, Tong; Kim, Donggyu. Orthogonal matroids over tracts. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e130. doi: 10.1017/fms.2025.10085
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