Quiver matroids are defined with morphisms and bundles; their F1-moduli spaces have point counts equaling the Euler characteristic of complex quiver Grassmannians in nice cases.
Tropical Incidence Relations, Polytopes, and Concordant Matroids
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this paper, we develop a tropical analog of the classical flag variety that we call the flag Dressian. We find relations, which we call "tropical incidence relations", for when one tropical linear space is contained in another, and show that the flag Dressian is a tropical prevariety. In the case of 2-step flag Dressians, which we call "tropical incidence prevarieties", we find an equivalence between points in this space and induced subdivisions of a hypersimplex, generalizing two parts of an equivalence given by D. Speyer for tropical linear spaces. We attempt to generalize the third part of Speyer's equivalence to concordant matroids and obtain some partial results.
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UNVERDICTED 2representative citing papers
Five equivalent characterizations of strong Δ-matroids are given, including novel peerless and isolated antipode conditions that yield new local exchange axioms, motivated by tropical equations from the orthogonal Grassmannian.
citing papers explorer
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Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\mathbb{F}_1$-points
Quiver matroids are defined with morphisms and bundles; their F1-moduli spaces have point counts equaling the Euler characteristic of complex quiver Grassmannians in nice cases.
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Characterisations of strong $\Delta$-matroids
Five equivalent characterizations of strong Δ-matroids are given, including novel peerless and isolated antipode conditions that yield new local exchange axioms, motivated by tropical equations from the orthogonal Grassmannian.