A proof of the linearity conjecture for k-blocking sets in PG(n, p(3)), p prime

作者：Lavrauw M^*; Storme L; de Voorde G Van

来源：Journal of Combinatorial Theory - Series A, 2011, 118(3): 808-818.

DOI：10.1016/j.jcta.2010.11.013

• Blocking sets
• Linear sets
• Linearity conjecture

In this paper, we show that a small minimal k-blocking set in PG(n, q(3)), q = p(h), h >= 1, p prime, p >= 7, intersecting every (n - k)-space in 1 (mod q) points, is linear. As a corollary, this result shows that all small minimal k-blocking sets in PG(n, p(3)), p prime, p >= 7, are F-p-linear, proving the linearity conjecture (see Sziklai, 2008 [9]) in the case PG(n, p(3)), p prime, p >= 7.

• 出版日期2011-4