Valuations for matroid polytope subdivisions

Abstract

We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.

19 pages. 2 figures; added section 6 + other corrections

Cited by in corpus (5)

• Chern-Schwartz-MacPherson cycles of matroids
• Valuative invariants for large classes of matroids
• Matroid relaxations and Kazhdan-Lusztig non-degeneracy
• The Universal Valuation of Coxeter Matroids
• Polyhedral and Tropical Geometry of Flag Positroids