TY - JOUR

T1 - On the number of flats spanned by a set of points in PG(d,q)

AU - Boros, Endre

AU - Meshulam, Roy

N1 - Funding Information:
~" Research supported in part by the Office of Naval Research (Grants NO0014-92-F-1375 and N00014-92-F-4083) and by the Air Force Office of Scientific Research (Grant F49620-93-1-0041 ). * Corresponding author. E-mail:boros@ruteor.rutgers.edu.

PY - 1996/4/6

Y1 - 1996/4/6

N2 - It is shown that for fixed 1 ≤ r ≤ s < d and ε > 0, if X ⊂ PG(d, q) contains (1 + ε)qs points, then the number of r-flats spanned by X is at least c(ε)q(r + 1)(s + 1 - r), i.e. a positive fraction of the number of r-flats in PG(s + 1, q).

AB - It is shown that for fixed 1 ≤ r ≤ s < d and ε > 0, if X ⊂ PG(d, q) contains (1 + ε)qs points, then the number of r-flats spanned by X is at least c(ε)q(r + 1)(s + 1 - r), i.e. a positive fraction of the number of r-flats in PG(s + 1, q).

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U2 - 10.1016/0012-365X(95)00206-C

DO - 10.1016/0012-365X(95)00206-C

M3 - Article

AN - SCOPUS:0041629403

SN - 0012-365X

VL - 150

SP - 407

EP - 409

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -