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Let be a real number and let denote the set of real numbers approximable at order at least by rational numbers. More than eighty years ago, Jarník and, independently, Besicovitch established that the Hausdorff dimension of is equal to . We investigate the size of the intersection of with Ahlfors regular compact subsets of the interval . In particular, we propose a conjecture for the exact value of the dimension of intersected with the middle-third Cantor set and give several results...
We design algorithms of “optimal" for several natural problems about first-order queries on structures of bounded degree. For that purpose, we first introduce a framework to deal with logical or combinatorial problems whose instances may admit of several solutions . One associates to such a problem several specific tasks: compute a (for the uniform probability distribution) solution ; without repetition each solution
in some specific linear order where ; compute the solution...
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