Abstract
Small tight sets have been classified in finite classical polar spaces of symplectic type, hyperbolic type and one of the two Hermitian types [1]. The approach used is not working for the remaining finite classical polar spaces, mainly due to the fact that a tight set for these is not necessarily a minihyper, so the known results on blocking sets can not be applied. This might be the reason that there is no classification for small tight sets in these spaces. This paper provides a classification of tight sets with parameter x in these spaces provided that x is small compared to the order q of the polar space. One of the results is that a tight set of the generalized quadrangle Q(4,q) that is not the union of disjoint lines has at least (\(\sqrt q \) + 1)(q + 1) points with equality if and only if it consists of the points of an embedded subquadrangle of order \(\sqrt q \).
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Metsch, K. Small tight sets in finite elliptic, parabolic and Hermitian polar spaces. Combinatorica 36, 725–744 (2016). https://doi.org/10.1007/s00493-015-3260-2
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DOI: https://doi.org/10.1007/s00493-015-3260-2