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.

Given an undirected graph G = (V,E) and a delta-matroid (V,F), the delta-matroid matching problem is to find a maximum cardinality matching M such that the set of the end vertices of M belongs to F . This problem is a natural generalization of the matroid matching problem to delta-matroids, and thus it cannot be solved in polynomial time in general. This paper introduces a class of the delta-ma...

The main purpose of this study is to discuss the uniform boundednessprinciple in fuzzifying topological linear spaces. At first theconcepts of uniformly boundedness principle and fuzzy equicontinuousfamily of linear operators are proposed, then the relations betweenfuzzy equicontinuous and uniformly bounded are studied, and with thehelp of net convergence, the characterization of fuzzyequiconti...

AND GENERIC RIGIDITY IN THE PLANE SACHIN PATKAR, BRIGITTE SERVATIUS, AND K. V. SUBRAHMANYAM Abstract. We consider the concept of abstract 2–dimensional rigidity and provide necessary and sufficient conditions for a matroid to be an abstract rigidity matroid of a complete graph. This characterization is a natural extenWe consider the concept of abstract 2–dimensional rigidity and provide necessa...

A 2-dimensional direction-length framework (G,p) consists of a multigraph G=(V;D,L) with realisation p:V→R2. The edges G represent geometric constraints: in L have fixed length, and D gradient. is globally rigid if every (G,q) which satisfies the same constraints as can be obtained from by an isometry plane. We characterise global rigidity for class frameworks p generic matroid connected. Speci...

The matroid parity (MP) problem is a natural extension of the matching problem to the matroid setting. It can be formulated as a 0− 1 linear program using the so-called rank and line constraints. We call the associated family of polytopes MP polytopes. We then prove the following: (i) when the matroid is a gammoid, each MP polytope is a projection of a perfect matching polytope into a suitable ...

We give an example of a simple oriented matroid D that admits an oriented adjoint. Already any adjoint of the underlying matroid D, however, does itself not admit an adjoint. D arises from the wellknown Non-Desargues-Matroid by a coextension by a coparallel element and, hence, has rank 4. The orientability of D and some of its adjoints follows from an apparantly new oriented matroid constructio...