Author
Stefano Innamorati
Bio: Stefano Innamorati is an academic researcher from University of L'Aquila. The author has contributed to research in topics: Blocking set & Projective space. The author has an hindex of 7, co-authored 22 publications receiving 127 citations.
Topics: Blocking set, Projective space, Quadric, Mathematics, Quadrangle
Papers
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TL;DR: A combinatorial technique to prove the uniqueness of certain configurations realizing largest minimal blocking sets is introduced and is applied to the first open case: theiqueness of a minimal blocking 19-set in PG(2,7).
13 citations
TL;DR: It is proved that in a projective space of dimension three and square order q 2 a-set of class 1, 2, ?
12 citations
TL;DR: It is proved that PG(2, 8) does not contain minimal blocking sets of size 14, which supports the conjecture that q2−q+ 2 is the largest size for a maximal partial spread of PG(3, q), q>7.
Abstract: We prove that PG(2, 8) does not contain minimal blocking sets of size 14. Using this result we prove that 58 is the largest size for a maximal partial spread of PG(3, 8). This supports the conjecture that q2−q+ 2 is the largest size for a maximal partial spread of PG(3, q), q>7.
12 citations
TL;DR: In this paper, a combinatorial characterization of the non-singular Hermitian variety H (4, q2) was obtained with a minimal incidence condition with respect to dimension two.
Abstract: This paper deals with (q7 + q5 + q2 + 1)-sets of type (m, n)3 in PG(4, q2), q > 2. Thus, with a minimal incidence condition with respect to dimension two, we obtain a combinatorial characterization of the non-singular Hermitian variety H (4, q2).
11 citations
TL;DR: In this article, a suitable "attraction" property is introduced to realize minimum blocking sets of a finite projective plane. But this property is not suitable for the case of infinite projective planes.
Abstract: Some results on configurations realizing minimum blocking sets of a finite projective plane are obtained by introducing a suitable “attraction” property.
10 citations
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TL;DR: This paper surveys the results on this problem of determining the possible cardinalities of minimal blocking sets and gives some new results (or new proofs) given.
Abstract: The spectrum problem for minimal blocking sets means that we wish to determine the possible cardinalities of minimal blocking sets. Besides surveying the results on this problem some new results (or new proofs) are given.
42 citations
TL;DR: In this article, a generalization of Buekenhout's construction of unitals is presented, which gives minimal blocking sets of size q4/3/3 + 1 or q 4/3+1 + 2 in non-prime order.
Abstract: The size of large minimal blocking sets is bounded by the Bruen–Thas upper bound. The bound is sharp when q is a square. Here the bound is improved if q is a non-square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non-prime order. The construction can be regarded as a generalization of Buekenhout's construction of unitals. For example, if q is a cube, then our construction gives minimal blocking sets of size q4/3 + 1 or q4/3 + 2. Density results for the spectrum of minimal blocking sets in Galois planes of non-prime order is also presented. The most attractive case is when q is a square, where we show that there is a minimal blocking set for any size from the interval . © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 25–41, 2005.
25 citations
TL;DR: Blokhuis and Storme as mentioned in this paper used Lacunary polynomials with algebraic curves to improve the known characterization results on multiple blocking sets and to prove a t (mod p) result on small t-fold blocking sets of PG(2, q = pn), p prime, n = 1.
Abstract: This article continues the study of multiple blocking sets in PG(2, q). In [A. Blokhuis, L. Storme, T. Szonyi, Lacunary polynomials, multiple blocking sets and Baer subplanes. J. London Math. Soc. (2) 60 (1999), 321–332. MR1724814 (2000j:05025) Zbl 0940.51007], using lacunary polynomials, it was proven that t-fold blocking sets of PG(2, q), q square, t
25 citations
TL;DR: In this article, a survey about q-analogues of some classical theorems in extremal set theory is presented, which are related to determining the chromatic number of the qanalogue of Kneser graphs.
Abstract: In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.
20 citations