Bases in oriented matroids

Completeness in oriented matroids

✍ William E. Fenton 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 665 KB

The oriented matroid is a structure combining the notions of independent set and opposite element. Dependence induces a closure operator which in the vector space model is the convex hull. Weak completeness is defined as having every maximal convex set contain a maximal subspace; completeness means

Oriented Lagrangian Matroids

✍ Richard F. Booth; Alexandre V. Borovik; Israel M. Gelfand; Neil White 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 201 KB

In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought of as stratifications of thin Schubert cells into unions of connected components. The definitions are made first in ter

On Greedy Bases Packing in Matroids

✍ Brahim Chaourar 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 169 KB

Let S be a finite set and M = (S, B) be a matroid where B is the set of its bases. We say that a basis B is greedy in M or the pair (M, B) is greedy if, for every sum of bases vector w, the coefficient: where B and its characteristic vector will not be distinguished, is integer. We define a notion

Max-balanced flows in oriented matroids

✍ Mark Hartmann; Michael H. Schneider 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 863 KB

Let M =(E, d~) be an oriented matroid on the ground set E. A real-valued vector x defined on E is a max-balanced flow for M if for every signed cocircuit Y~(.9 ±, we have maxe~y+xe=maxe~r-x e. We extend the admissibility and decomposition theorems of Hamacher from regular to general oriented matroid

Large convex sets in oriented matroids

✍ J.Richard Buchi; William E Fenton 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 653 KB

Equicovering matroids by distinct bases

✍ Pierre Fraisse; Pavol Hell 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 206 KB