منابع مشابه
Projective geometries in dense matroids
We prove that, given integers l, q ≥ 2 and n there exists an integer α such that, if M is a simple matroid with no l + 2point line minor and at least αq elements, then M contains a PG(n− 1, q′)-minor, for some prime-power q′ > q.
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 کاملProjective geometries in exponentially dense matroids. II
We show for each positive integer a that, if M is a minor-closed class of matroids not containing all rank-(a+ 1) uniform matroids, then there exists an integer c such that either every rank-r matroid in M can be covered by at most r rank-a sets, or M contains the GF(q)-representable matroids for some prime power q and every rank-r matroid inM can be covered by at most cq rank-a sets. In the la...
متن کاملMatroids Denser than a Projective Geometry
The growth-rate function for a minor-closed class M of matroids is the function h where, for each non-negative integer r, h(r) is the maximum number of elements of a simple matroid in M with rank at most r. The Growth-Rate Theorem of Geelen, Kabell, Kung, and Whittle shows, essentially, that the growth-rate function is always either linear, quadratic, exponential with some prime power q as the ...
متن کاملA Characterization of the Orientations of Ternary Matroids
A matroid or oriented matroid is dyadic if it has a rational representation with all nonzero subde-terminants in ff2 k : k 2 Zg. Our main theorem is that an oriented matroid is dyadic if and only if the underlying matroid is ternary. A consequence of our theorem is the recent result of G. Whittle that a rational matroid is dyadic if and only if it is ternary. Along the way, we establish that ea...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1995
ISSN: 0001-8708
DOI: 10.1006/aima.1995.1036