Minimal non-orientable matroids of rank three
نویسندگان
چکیده
منابع مشابه
Some minimal non - orientable matroids of rank three by Günter M . Ziegler
We construct an infinite family of minor-minimal rank three matroids that are not orientable.
متن کاملMinimal non-orientable matroids in a projective plane
The study of non-orientable matroids has not received very much attention compared with the study of representable matroids or oriented matroids. Proving non-orientability of a matroid is known to be a difficult problem even for small matroids of rank 3. RichterGebert [4] even proved that this problem is NP-complete. In general, there are only some necessary conditions (Proposition 6.6.1 of [1]).
متن کاملRank-Three Matroids are Rayleigh
A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.
متن کاملEulerian and Bipartite Orientable Matroids
Further work of Brylawski and Heron (see [4, p. 315]) explores other characterizations of Eulerian binary matroids. They showed, independently, that a binary matroid M is Eulerian if and only if its dual, M∗, is a binary affine matroid. More recently, Shikare and Raghunathan [5] have shown that a binary matroid M is Eulerian if and only if the number of independent sets of M is odd. This chapte...
متن کاملOriented Rank Three Matroids and Projective Planes
Quite recently, GOODMAN, POLLACK, WENGER and ZAMFIRESCU [7], [8] have proven two conjectures by GRÜNBAUM right, showing that any arrangement of pseudolines in the plane can be embedded into a flat projective plane and that there exists a universal topological projective plane in which every arrangement of pseudolines is stretchable. By FOLKMAN and LAWRENCE's theorem [6], this plane contains eve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2015
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2015.03.025