AbstractA set of axioms of defining a matroid in terms of its bases is given by the Steinitz exchange lemma. In this paper, we show these axioms are not independent, and find a subcollection defining the same structure.A special motivation is given by the Graβmann variety and by oriented matroids, where we present improved versions of known results
Also published as: SFB-303--95841SIGLEAvailable from TIB Hannover: RN 4052(95841) / FIZ - Fachinform...
AbstractFocusing on the interplay between properties of the Grassmann variety and properties of matr...
AbstractWe define the concept of unique exchange on a sequence (X1,…, Xm) of bases of a matroid M as...
AbstractA set of axioms of defining a matroid in terms of its bases is given by the Steinitz exchang...
AbstractWe introduce new basis exchange axioms for matroids and oriented matroids. These new axioms ...
AbstractTheorem. Given two basesB1andB2of a matroid (M, r), and a partitionB1 = X1 ∪ Y1, there is a ...
The purpose of this note is to point out that the subset exchange property of matroid bases is a spe...
Recently Dress and Wenzel introduced the concept of valuated matroid in terms of a quantitative exte...
AbstractA matroid may be defined as a collection of sets, called bases, which satisfy a certain exch...
Abstract“Convex analysis” is developed for functions defined on integer lattice points. We investiga...
AbstractΔ-matroids are set systems which arise, e.g., in the study of greedy algorithms. Similarly t...
Two further equivalent axioms are given for valuations of a matroid. Let M = (V,B) be a matroid on a...
“Convex analysis” is developed for functions defined on integer lattice points. We investigate the c...
AbstractThe bases and the cocircuits of a matroid form a blocking pair of clutters; this fact leads ...
AbstractTheorem. Given two basesB1andB2of a matroid (M, r), and a partitionB1 = X1 ∪ Y1, there is a ...
Also published as: SFB-303--95841SIGLEAvailable from TIB Hannover: RN 4052(95841) / FIZ - Fachinform...
AbstractFocusing on the interplay between properties of the Grassmann variety and properties of matr...
AbstractWe define the concept of unique exchange on a sequence (X1,…, Xm) of bases of a matroid M as...
AbstractA set of axioms of defining a matroid in terms of its bases is given by the Steinitz exchang...
AbstractWe introduce new basis exchange axioms for matroids and oriented matroids. These new axioms ...
AbstractTheorem. Given two basesB1andB2of a matroid (M, r), and a partitionB1 = X1 ∪ Y1, there is a ...
The purpose of this note is to point out that the subset exchange property of matroid bases is a spe...
Recently Dress and Wenzel introduced the concept of valuated matroid in terms of a quantitative exte...
AbstractA matroid may be defined as a collection of sets, called bases, which satisfy a certain exch...
Abstract“Convex analysis” is developed for functions defined on integer lattice points. We investiga...
AbstractΔ-matroids are set systems which arise, e.g., in the study of greedy algorithms. Similarly t...
Two further equivalent axioms are given for valuations of a matroid. Let M = (V,B) be a matroid on a...
“Convex analysis” is developed for functions defined on integer lattice points. We investigate the c...
AbstractThe bases and the cocircuits of a matroid form a blocking pair of clutters; this fact leads ...
AbstractTheorem. Given two basesB1andB2of a matroid (M, r), and a partitionB1 = X1 ∪ Y1, there is a ...
Also published as: SFB-303--95841SIGLEAvailable from TIB Hannover: RN 4052(95841) / FIZ - Fachinform...
AbstractFocusing on the interplay between properties of the Grassmann variety and properties of matr...
AbstractWe define the concept of unique exchange on a sequence (X1,…, Xm) of bases of a matroid M as...
DOI
Add to ORKG