Oriented Lagrangian matroids. (English) Zbl 0990.52003
This paper provides an “oriented” extension of the theory of “Lagrangian symplectic matroids” of A. V. Borovik, J. Gelfand and N. White [J. Algebr. Combinatorics 8, No. 3, 235-252 (1998; Zbl 0919.05012)]. The prime examples are derived from the non-zero principal minors of a real symmetric matrix.
The results of this paper include combinatorial and geometric characterizations (in terms of subpolytopes of the \(n\)-cube \([-1, +1]^n\)).
The results of this paper include combinatorial and geometric characterizations (in terms of subpolytopes of the \(n\)-cube \([-1, +1]^n\)).
Reviewer: Günter M.Ziegler (Berlin)
MSC:
| 52C40 | Oriented matroids in discrete geometry |
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
| 52A01 | Axiomatic and generalized convexity |
Keywords:
oriented matroids; Coxeter matroids; basis polytopes; Lagrangian matroids; delta-matroids; symplectic matroidsCitations:
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