Abstract
In many point-line geometries, to cover all points except one, more lines are needed than to cover all points. Bounds can be given by looking at the dimension of the space of functions induced by polynomials of bounded degree.
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Alon, N., Füredi, Z.: Covering the cube by affine hyperplanes. Eur. J. Comb. 14, 79–83 (1993)
Ball, S.: Polynomials in finite geometries. In: Lamb, J.D., Preece, D.A. (eds.) Surveys in Combinatorics, pp. 17–36 (1999)
Ball, S., Serra, O.: Punctured combinatorial Nullstellensätze. Combinatorica (2009, to appear)
Beutelspacher, A.: On t-covers in finite projective spaces. J. Geom. 12, 10–16 (1979)
Blokhuis, A., Brouwer, A.E., Wilbrink, H.A.: Blocking sets in PG(2,p) for small p, and partial spreads in PG(3,7). Adv. Geom. Suppl. S245–S253 (2003). Special issue dedicated to Adriano Barlotti
Brouwer, A.E., Schrijver, A.: The blocking number of an affine space. J. Comb. Theory, Ser. A 24, 251–253 (1978)
Dodunekov, S., Storme, L., Van de Voorde, G.: Partial covers of PG(n,q). Preprint, August 2008
Eisfeld, J.: On smallest covers of finite projective spaces. Arch. Math. 68, 77–80 (1997)
Jamison, R.E.: Covering finite fields with cosets of subspaces. J. Comb. Theory, Ser. A 22, 253–266 (1977)
Krčadinac, V.: Steiner 2-designs S(2,4,28) with nontrivial automorphisms. Glas. Mat. 37(57), 259–268 (2002)
Lovász, L.: On the ratio of optimal integral and fractional covers. Discrete Math. 13, 383–390 (1975)
Thas, J.A.: A combinatorial characterization of Hermitian curves. J. Algebr. Comb. 1, 97–102 (1992)
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Blokhuis, A., Brouwer, A.E. & Szőnyi, T. Covering all points except one. J Algebr Comb 32, 59–66 (2010). https://doi.org/10.1007/s10801-009-0204-1
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DOI: https://doi.org/10.1007/s10801-009-0204-1