In this paper we address two of the major foundational questions in the theory of matroids over rings. First, we provide a cryptomorphic axiomatisation, by introducing an analogue of the base polytope for matroids. Second, we describe a parameter space for matroids over a valuation ring, which turns out to be a tropical version of the Bott-Samelson varieties for the full flag variety. Thus a matroid over a valuation ring is a sequence of flags of tropical linear spaces a.k.a. valuated matroids.

Polyhedra and parameter spaces for matroids over valuation rings / Fink A; Moci L. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 343:(2019), pp. 448-494. [10.1016/j.aim.2018.11.009]

Polyhedra and parameter spaces for matroids over valuation rings

Moci L
2019

Abstract

In this paper we address two of the major foundational questions in the theory of matroids over rings. First, we provide a cryptomorphic axiomatisation, by introducing an analogue of the base polytope for matroids. Second, we describe a parameter space for matroids over a valuation ring, which turns out to be a tropical version of the Bott-Samelson varieties for the full flag variety. Thus a matroid over a valuation ring is a sequence of flags of tropical linear spaces a.k.a. valuated matroids.
2019
Polyhedra and parameter spaces for matroids over valuation rings / Fink A; Moci L. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 343:(2019), pp. 448-494. [10.1016/j.aim.2018.11.009]
Fink A; Moci L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/676967
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