The Number of Points in a Combinatorial Geometry with No 8-point-line Minors
نویسندگان
چکیده
We show that when n is greater than 3, the number of points in a combinatorial geometry (or simple matroid) G of rank n containing no minor isomorphic to the 8-point line is at most 1 4 (5n − 1). This bound is sharp and is attained if and only if the geometry G is the projective geometry PG(n − 1, 5) over the field GF(5). This paper appeared in: Mathematical Essays in Honor of Gian-Carlo Rota, B. Sagan and R. P. Stanley, eds., Birkhauser, 1998, 271–284.
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