✦ LIBER ✦

A homotopy theorem on oriented matroids

✍ Scribed by R. Cordovil; M.L. Moreira

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 348 KB
Volume: 111
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90149-n

No coin nor oath required. For personal study only.

✦ Synopsis

Consider a finite family of hyperplanes _%? = {Hi, . _. , H,} in the finite-dimensional vector space IWd. We call chambers (determined by 2) the connected components of W"\ U y=, Hi. Galleries are finite families of chambers (C,,,C,, , C,), where exactly one hyperplane separates Ci+i from Ci, for O<i<m, and exactly m hyperplanes separate C, from C,. Using oriented matroid theory, we prove that any two galleries with the same extremities can be derived from each other by a finite number of deformations of the same kind (elementary deformations). When the chambers are simplicial cones, this is a result of Deligne (1972). Our theorem generalizes also a result of .

📜 SIMILAR VOLUMES

Separation theorems for oriented matroid

Separation theorems for oriented matroids

✍ Achim Bachem; Alfred Wanka 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 877 KB

In this paper we show that Minty's lemma can be used to prove the Hahn-Banach theorem as well as other theorems in this class such as Radon's and Heiiy's theorem for oriented matroids having an intersection property which guarantees that every pair of flats intersects in some point extension 6 Up of

Invariant Theory-like Theorems for Matro

Invariant Theory-like Theorems for Matroids and Oriented Matroids

✍ J. Bokowski; A.G. Deoliveira 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 394 KB

Theorems on matroid connectivity

✍ T. Inukai; L. Weinberg 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 135 KB

On a Mutation Problem for Oriented Matro

On a Mutation Problem for Oriented Matroids

✍ Jürgen Bokowski; Holger Rohlfs 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 469 KB

For uniform oriented matroids M with n elements, there is in the realizable case a sharp lower bound L r (n) for the number mut(M) of mutations of M : L r (n) = n ≤ mut(M), see Shannon [17]. Finding a sharp lower bound L(n) ≤ mut(M) in the non-realizable case is an open problem for rank d ≥ 4. Las V

On the Folkman–Lawrence Topological Repr

On the Folkman–Lawrence Topological Representation Theorem for Oriented Matroids of Rank 3

✍ Jürgen Bokowski; Susanne Mock; Ileana Streinu 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 241 KB

We present a new direct proof of the Folkman-Lawrence topological representation theorem for oriented matroids of rank 3.

Comparison Theorems in Homotopy Theory V

Comparison Theorems in Homotopy Theory Via Operations on Homotopy Sets

✍ A. J. Berrick; K. H. Kamps 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 293 KB

In this paper we present comparison theorems in semicubical homotopy theory. Topological versions are more or less well known and have been obtained amongst others by A. DOLD (IS], [7]), I. M. JAMES ([Ill), P. R. HEATH ([9]), S. P. LAM ([15]), and the first author ([Z], [3]). A partially abstract ap