Maximal partial spreads and transversal-free translation nets
نویسندگان
چکیده
منابع مشابه
Infinite Maximal Partial Spreads
The concept of ‘critical deficiency’ of a finite net is generalized to the infinite case and a variety of infinite maximal partial spreads are constructed.
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We prove Heden’s result that the deficiency δ of a maximal partial spread in PG(3, q) is greater than 1+ 1 2 (1+ √ 5)q unless δ−1 is a multiple of p, where q = p. When q is odd and not a square, we are able to improve this lower bound to roughly √ 3q.
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Some constructions of maximal partial spreads of finite classical polar spaces are provided. In particular we show that, for n > 1, H(4n−1, q2) has a maximal partial spread of size q2n + 1, H(4n + 1, q2) has a maximal partial spread of size q2n+1 + 1 and, for n > 2, Q+(4n − 1, q), Q(4n − 2, q), W(4n − 1, q), q even, W(4n − 3, q), q even, have a maximal partial spread of size qn + 1.
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For n ≥ 9, we construct maximal partial line spreads for non-singular quadrics of PG(n, q) for every size between approximately (cn + d)(qn−3 + qn−5) log 2q and qn−2, for some small constants c and d. These results are similar to spectrum results on maximal partial line spreads in finite projective spaces by Heden, and by Gács and Szőnyi. These results also extend spectrum results on maximal pa...
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A lower bound for the size of a maximal partial spread of H(2n+1, q) is given. For H(2n + 1, q) in general, and for H(5, q) in particular, new upper bounds for this size are also obtained. In [1], maximal partial spreads of H(3, q) and H(5, q) have been constructed from spreads of W3(q) and W5(q) respectively; the construction for H(5, q) will be generalized to H(4n+ 1, q), n ≥ 1, thus yielding...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1993
ISSN: 0097-3165
DOI: 10.1016/0097-3165(93)90072-g