Relative width measures and the plank problem
نویسندگان
چکیده
منابع مشابه
Tarski's Plank Problem Revisited
In the 1930's, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric and analytic aspects of coverings by planks in the present time as well. The paper is a survey type with a list of open research problems.
متن کاملTarski ’ s Plank Problem Revisited
In the 1930’s, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski’s question and its variants continue to generate interest in the geometric and analytic aspects of coverings by planks in the present time as well. The paper is of a survey type with some new results and with a list of open research problems on the ...
متن کاملThe Plank Problem for Symmetric Bodies
Given a symmetric convex body C and n hyperplanes in an Euclidean space, there is a translate of a multiple of C, at least 1 n+1 times as large, inside C, whose interior does not meet any of the hyperplanes. The result generalizes Bang's solution of the plank problem of Tarski and has applications to Diophantine approximation.
متن کاملComparing the Relative Volume with the Relative Inradius and the Relative Width
We consider subdivisions of a convex bodyG in two subsets E andG \E. We obtain several inequalities comparing the relative volume: (1) with the minimum relative inradius, (2) with the maximum relative inradius, (3) with the minimum relative width, and (4) with the maximum relative width. In each case, we obtain the best upper and lower estimates for subdivisions determined by general hypersurfa...
متن کاملClique-Width and Directed Width Measures for Answer-Set Programming
Disjunctive Answer Set Programming (ASP) is a powerful declarative programming paradigm whose main decision problems are located on the second level of the polynomial hierarchy. Identifying tractable fragments and developing efficient algorithms for such fragments are thus important objectives in order to complement the sophisticated ASP systems available to date. Hard problems can become tract...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1988
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1988.135.299