On the decidability of Diophantine problems in combinatorial geometry
نویسندگان
چکیده
منابع مشابه
On the Decidability of Diophantine Problems in Combinatorial Geometry
In spite of Matiyasevic's solution to Hubert's 10th problem some fifteen years ago it is still unknown whether there exists an algorithm to decide the solvability of diophantine equations within the field of rational numbers. In this note we show the equivalence of this problem with a conjecture of B. Grünbaum [6] on rational coordinatizability in combinatorial geometry. Such an algorithm exist...
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Combinatorial Problems in Computational Geometry
In this thesis we study a variety of problems in combinatorial and computational geometry, which deal with various aspects of arrangements of geometric objects, in the plane and in higher dimensions. Some of these problems have algorithmic applications, while others provide combinatorial bounds for various structures in such arrangements. The thesis involves two main themes: (i) Counting Crossi...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1987
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1987-15532-7