منابع مشابه
Complete Arcs in Steiner Triple Systems
A complete arc in a design is a set of elements which contains no block, and is maximal with respect to this property. The spectrum of sizes of complete arcs in Steiner triple systems is determined without exception here.
متن کاملSmall Complete Arcs in Projective Planes
In the late 1950’s, B. Segre introduced the fundamental notion of arcs and complete arcs [48, 49]. An arc in a finite projective plane is a set of points with no three on a line and it is complete if cannot be extended without violating this property. Given a projective plane P, determining n(P), the size of its smallest complete arc, has been a major open question in finite geometry for severa...
متن کاملOn Complete Arcs Arising from Plane Curves
We point out an interplay between Fq-Frobenius non-classical plane curves and complete (k, d)-arcs in P2(Fq). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q − d + 2) and d = (q − 1)/(q − 1), q being a power of the characteristic. In addi...
متن کاملThe complete arcs of PG(2,31)
We obtained a full computer classification of all complete arcs in the Desarguesian projective plane of order 31 using essentially the same methods as for earlier results for planes of smaller order, i.e., isomorph-free backtracking using canonical augmentation. We tabulate the resulting numbers of complete arcs according to size and automorphism group. We give explicit descriptions for all com...
متن کاملOn large complete arcs: odd case
An approach to the computations of upper bounds on the size of large complete arcs is presented. In particular, we obtain geometrical properties of irreducible envelopes associated to a second largest complete arc provided that the order of the underlying field is large enough.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00330-5