Projects per year
Abstract
Intrinsic Diophantine approximation on fractals, such as the Cantor ternary set, was undoubtedly motivated by questions asked by K. Mahler (1984). One of the main goals of this paper is to develop and utilize the theory of infinite de Bruijn sequences in order to answer closely related questions. In particular, we prove that the set of infinite de Bruijn sequences in $k\geq 2$ letters, thought of as a set of real numbers via a decimal expansion, has positive Hausdorff dimension. For a given $k$, these sequences bear a strong connection to Diophantine approximation on certain fractals. In particular, the optimality of an intrinsic Dirichlet function on these fractals with respect to the height function defined by symbolic representations of rationals follows from these results.
Original language  English 

Pages (fromto)  271293 
Number of pages  23 
Journal  ANNALS OF COMBINATORICS 
Volume  22 
Issue number  2 
Early online date  27 Apr 2018 
DOIs  
Publication status  Published  1 Jun 2018 
Bibliographical note
© 2018 The Author(s)Keywords
 math.CO
 math.NT
Projects
 1 Finished

Programme GrantNew Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research