Maximal partial spreads and the modular n-queen problem III
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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In this paper we construct maximal partial spreads in PG(3, q) which are a log q factor larger than the best known lower bound. For n ≥ 5 we also construct maximal partial spreads in PG(n, q) of each size between cnqn−2 log q and c′qn−1.
متن کاملHeden's bound on maximal partial spreads
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.
متن کاملMaximal Partial Spreads of Polar Spaces
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.
متن کاملMaximal partial line spreads of non-singular quadrics
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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00464-7