منابع مشابه
Small 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...
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We use arcs found by Storme and van Maldeghem in their classification of primitive arcs in PG(2, q) as seeds for constructing small complete arcs in these planes. Our complete arcs are obtained by taking the union of such a “seed arc” with some orbits of a subgroup of its stabilizer. Using this approach we construct five different complete 15arcs fixed by Z3 in PG(2, 37), a complete 20-arc fixe...
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Recent results on blocking sets are applied to the bisecants of a small complete arc, since these lines form a dual blocking set. It is shown that such blocking sets yield a lacunary polynomial of specific type. This leads to an improvement to the lower bound of the existence of a complete k-arc when the order of the plane is a square prime.
متن کاملVeronesean Almost Binomial Almost Complete Intersections
The second Veronese ideal In contains a natural complete intersection Jn generated by the principal 2-minors of a symmetric (n× n)-matrix. We determine subintersections of the primary decomposition of Jn where one intersectand is omitted. If In is omitted, the result is the other end of a complete intersection link as in liaison theory. These subintersections also yield interesting insights int...
متن کاملAlmost Complete Sets
We show that there is a set which is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2. Here a set A in a complexity class C is almost complete for C under some reducibility r if the class of the problems in C which do not r-reduce to A has measure 0 in C in the sense of Lutz’s resource-bounded measure the...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00412-5