ALGEBRAIC-VARIETIES CHARACTERIZING MATROIDS AND ORIENTED MATROIDS

• Type: Article in International Scientific Journal
• Date: 1991

Authors

BOKOWSKI, J (Author) Other; DEOLIVEIRA, AG (Author) FCUP; RICHTERGEBERT, J (Author) Other

Journal

Title: Advances in Mathematics

Vol. 87

Pages: 160-185

ISSN: 0001-8708

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-QNS

DOI: 10.1016/0001-8708(91)90070-n

Abstract (EN): Focusing on the interplay between properties of the Grassmann variety and properties of matroids and oriented matroids, this paper brings forward new algebraic methods in the theory of matroids and in the theory of oriented matroids; we introduce new algebraic varieties characterizing matroids and oriented matroids in the most general case. This new concept admits a systematic study of matroids and oriented matroids by using additional methods from calculus, algebra, and stochastics. An interesting new insight when the matroid variety over GF2 and the chirotope variety over GF3 are used shows that oriented matroids and matroids differ exactly by the underlying field. We investigate also a chirotope variety over R, its dimension, and its relation to the Grassmann variety. To find efficient algorithms in computational synthetic geometry, a crucial step lies in finding a small number of conditions for defining oriented matroids. Our new algebraic framework yields new results and straightforward proofs in this direction. © 1991.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 26