A density Hales-Jewett theorem for matroids
نویسندگان
چکیده
We show that if α is a positive real number, n and ` are integers exceeding 1, and q is a prime power, then every simple matroid M of sufficiently large rank, with no U2,`-minor, no rank-n projective geometry minor over a larger field than GF(q), and at least αq elements, has a rank-n affine geometry restriction over GF(q). This result can be viewed as an analogue of the multidimensional density Hales-Jewett theorem for matroids.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 112 شماره
صفحات -
تاریخ انتشار 2015