منابع مشابه
Collinear Points in Permutations
Consider the following problem: how many collinear triples of points must a transversal of Zn×Zn have? This question is connected with venerable issues in discrete geometry. We show that the answer, for n prime, is between (n− 1)/4 and (n − 1)/2, and consider an analogous question for collinear quadruples. We conjecture that the upper bound is the truth and suggest several other interesting pro...
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This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of n points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help with other problems, such as point line cover and general position subset selection. The classic topological sweeping algorithm of Edelsbrunner and Guibas can ...
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2 CM points on quaternion algebras 4 2.1 CM points, special points and reduction maps . . . . . . . . . 4 2.1.1 Quaternion algebras. . . . . . . . . . . . . . . . . . . . 4 2.1.2 Algebraic groups. . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Adelic groups. . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.4 Main objects. . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.5 Galois action...
متن کاملMany collinear k - tuples with no k + 1 collinear points József
For every k > 3, we give a construction of planar point sets with many collinear k-tuples and no collinear (k + 1)-tuples. We show that there are n0 = n0(k) and c = c(k) such that if n ≥ n0, then there exists a set of n points in the plane that does not contain k + 1 points on a line, but it contains at least n 2− c √ logn collinear k-tuples of points. Thus, we significantly improve the previou...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2017
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2017.11.1047