https://www.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
Extra Form
Lecturer 김동한
Dept. 동국대
date Oct 27, 2016

We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest return time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words by means of this function. Then, we establish a new result on repetitions in Sturmian words and show that it is best possible. We deduce a lower bound for the irrationality exponent of real numbers whose sequence of b-ary digits is a Sturmian sequence over {0,1,…,b-1} and we prove that this lower bound is best possible. If the irrationality exponent of \xi is equal to 2 or slightly greater than 2, then the b-ary expansion of \xi cannot be `too simple', in a suitable sense. Our result applies, among other classical numbers, to badly approximable numbers, non-zero rational powers of e, and log(1+1/a), provided that the integer a is sufficiently large. It establishes an unexpected connection between the irrationality exponent of a real number and its b-ary expansion.


  1. Seoul ICM 2014 유치과정 개요 및 준비전략

  2. Sheaf quantization of Hamiltonian isotopies and non-displacability problems

  3. Solver friendly finite element methods

  4. Space.Time.Noise

  5. Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures

  6. Structural stability of meandering-hyperbolic group actions

  7. Structures of Formal Proofs

  8. Study stochastic biochemical systems via their underlying network structures

  9. Subgroups of Mapping Class Groups

  10. 03Nov
    by 김수현
    in Math Colloquia

    Subword complexity, expansion of real numbers and irrationality exponents

  11. Sums of squares in quadratic number rings

  12. Survey on a geography of model theory

  13. Symmetry Breaking in Quasi-1D Coulomb Systems

  14. Symplectic Geometry, Mirror symmetry and Holomorphic Curves

  15. Symplectic topology and mirror symmetry of partial flag manifolds

  16. The classification of fusion categories and operator algebras

  17. The lace expansion in the past, present and future

  18. The Lagrange and Markov Spectra of Pythagorean triples

  19. The Mathematics of the Bose Gas and its Condensation

  20. The phase retrieval problem

Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 Next
/ 12