Symmetric designs, polarities and sub-designs
نویسندگان
چکیده
منابع مشابه
Unitals and Unitary Polarities in Symmetric Designs
We extend the notion of unital as well as unitary polarity from finite projective planes to arbitrary symmetric designs. The existence of unitals in several families of symmetric designs has been proved. It is shown that if a unital in a point-hyperplane design PGd−1(d, q) exists, then d = 2 or 3; in particular, unitals and ovoids are equivalent in case d = 3. Moreover, unitals have been found ...
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We prove that every polarity of PG(2k − 1, q), where k ≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to PGk(2k, q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada’s conjecture, for any field of prime order p. P...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90027-1