منابع مشابه
Lattice Packing in the Plane without Crossing Arcs
Introduction. We first review some definitions and results of Chalk and Rogers.2 If S and T are two sets of points in Euclidean »-space, then S+T will denote the set of all points s+t where s is in 5 and / is in T, while S— T is composed of all s — t. The point set sum will be denoted by 5UF and the intersection by SC\T. Let A be a lattice; then 5+A is a lattice packing if no two sets 5+X and 5...
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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 کاملOn small complete arcs in a finite plane
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.
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Let $T$ be a non-trivial tournament. An arc is emph{$t$-pancyclic} in $T$, if it is contained in a cycle of length $ell$ for every $tleq ell leq |V(T)|$. Let $p^t(T)$ denote the number of $t$-pancyclic arcs in $T$ and $h^t(T)$ the maximum number of $t$-pancyclic arcs contained in the same Hamiltonian cycle of $T$. Moon ({em J. Combin. Inform. System Sci.}, {bf 19} (1994), 207-214) showed that $...
متن کاملMinimizing the Number of Arcs Linking a Permutation of Points in the Plane
Given a finite set of points P in R and a permutation of P , f : P → P , what is the minimum number of arcs required to connect the points of P such that every point p ∈ P is adjacent to f(p) along an arc and no two arcs cross? We show this question is NP-complete. 1 Problem Definition An arc consists of a closed continuous subset of a circle in the plane (the subset may be a complete circle). ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.08.007