 Author
 Anamari Nakić and Leo Storme (UGent)
 Organization
 Abstract
 We show that every itight set in the Hermitian variety H(2r + 1, q) is a union of pairwise disjoint (2r + 1)dimensional Baer subgeometries PG(2r + 1, root q) and generators of H(2r + 1, q), if q >= 81 is an odd square and i < (q(2/3)  1)/2. We also show that an itight set in the symplectic polar space W(2r + 1, q) is a union of pairwise disjoint generators of W(2r + 1, q), pairs of disjoint rspaces {Delta,Delta(perpendicular to)}, and (2r + 1)dimensional Baer subgeometries. For W(2r + 1, q) with r even, pairs of disjoint rspaces {Delta,Delta(perpendicular to)} cannot occur. The (2r + 1)dimensional Baer subgeometries in the itight set of W(2r + 1, q) are invariant under the symplectic polarity perpendicular to of W(2r + 1, q) or they arise in pairs of disjoint Baer subgeometries corresponding to each other under perpendicular to. This improves previous results where i < q(5/8)/root 2+ 1 was assumed. Generalizing known techniques and using recent results on blocking sets and minihypers, we present an alternative proof of this result and consequently improve the upper bound on i to (q(2/3)  1)/2. We also apply our results on tight sets to improve a known result on maximal partial spreads in W(2r + 1, q).
 Keywords
 Tight sets, finite classical polar spaces, minihypers, blocking sets, Hermitian varieties, symplectic polar spaces, MULTIPLE BLOCKING SETS, BAER SUBPLANES, MINIHYPERS, ARCS
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8517621
 MLA
 Nakić, Anamari, and Leo Storme. “Tight Sets in Finite Classical Polar Spaces.” ADVANCES IN GEOMETRY 17.1 (2017): 109–129. Print.
 APA
 Nakić, A., & Storme, L. (2017). Tight sets in finite classical polar spaces. ADVANCES IN GEOMETRY, 17(1), 109–129.
 Chicago authordate
 Nakić, Anamari, and Leo Storme. 2017. “Tight Sets in Finite Classical Polar Spaces.” Advances in Geometry 17 (1): 109–129.
 Chicago authordate (all authors)
 Nakić, Anamari, and Leo Storme. 2017. “Tight Sets in Finite Classical Polar Spaces.” Advances in Geometry 17 (1): 109–129.
 Vancouver
 1.Nakić A, Storme L. Tight sets in finite classical polar spaces. ADVANCES IN GEOMETRY. 2017;17(1):109–29.
 IEEE
 [1]A. Nakić and L. Storme, “Tight sets in finite classical polar spaces,” ADVANCES IN GEOMETRY, vol. 17, no. 1, pp. 109–129, 2017.
@article{8517621, abstract = {{We show that every itight set in the Hermitian variety H(2r + 1, q) is a union of pairwise disjoint (2r + 1)dimensional Baer subgeometries PG(2r + 1, root q) and generators of H(2r + 1, q), if q >= 81 is an odd square and i < (q(2/3)  1)/2. We also show that an itight set in the symplectic polar space W(2r + 1, q) is a union of pairwise disjoint generators of W(2r + 1, q), pairs of disjoint rspaces {Delta,Delta(perpendicular to)}, and (2r + 1)dimensional Baer subgeometries. For W(2r + 1, q) with r even, pairs of disjoint rspaces {Delta,Delta(perpendicular to)} cannot occur. The (2r + 1)dimensional Baer subgeometries in the itight set of W(2r + 1, q) are invariant under the symplectic polarity perpendicular to of W(2r + 1, q) or they arise in pairs of disjoint Baer subgeometries corresponding to each other under perpendicular to. This improves previous results where i < q(5/8)/root 2+ 1 was assumed. Generalizing known techniques and using recent results on blocking sets and minihypers, we present an alternative proof of this result and consequently improve the upper bound on i to (q(2/3)  1)/2. We also apply our results on tight sets to improve a known result on maximal partial spreads in W(2r + 1, q).}}, author = {{Nakić, Anamari and Storme, Leo}}, issn = {{1615715X}}, journal = {{ADVANCES IN GEOMETRY}}, keywords = {{Tight sets,finite classical polar spaces,minihypers,blocking sets,Hermitian varieties,symplectic polar spaces,MULTIPLE BLOCKING SETS,BAER SUBPLANES,MINIHYPERS,ARCS}}, language = {{eng}}, number = {{1}}, pages = {{109129}}, title = {{Tight sets in finite classical polar spaces}}, url = {{http://dx.doi.org/10.1515/advgeom20160034}}, volume = {{17}}, year = {{2017}}, }
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