Submission date: 20 September 2017

Abstract:

We use (variations on) Mason's α-function as a pre-dimension function to construct new examples of ω-stable planes (i.e. simple rank 3 matroids). Specifically, we construct infinitely many ω-stable planes P(n), for n < ω, such that every finite plane is &or:-embeddable into P(n) for co-finitely many n < ω. As a consequence, for co-finitely many n < ω, the plane P(n) is neither projective, nor affine, nor linear, nor algebraic.

Mathematics Subject Classification: 03C45, 05B35

Keywords and phrases:

Full text arXiv 1709.06789: pdf, ps.