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Extra Form
강연자 김동한
소속 동국대
date 2016-10-27

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.


List of Articles
카테고리 제목 소속 강연자
수학강연회 학부생을 위한 ε 강연회: Sir Isaac Newton and scientific computing file 서울대학교 신동우
수학강연회 Existence of positive solutions for φ-Laplacian systems file 이용훈 수학강연회,특별강연,대중강연
BK21 FOUR Rookies Pitch 2021-2 Rookies Pitch: Regularity for PDEs (수미야) file 서울대학교 수미야
수학강연회 학부생을 위한 강연: Choi's orthogonal Latin Squares is at least 61 years earlier than Euler's file 연세대학교 송홍엽
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Algebraic Topology (송종백) file 고등과학원 송종백
수학강연회 행렬함수 Permanent의 극소값 결정과 미해결 문제들 file 제주대학교/서울대학교 송석준
수학강연회 L-function: complex vs. p-adic file 충북대학교 선해상
수학강연회 Quantitative residual non-vanishing of special values of various L-functions file UNIST 선해상
수학강연회 Mixing time of random processes file 서울대 서인석
수학강연회 <2020년도 젊은 과학자상 수상 기념강연> Metastability of stochastic systems file 서울대학교 서인석
수학강연회 W-algebras and related topics file 서울대학교 서의린
BK21 FOUR Rookies Pitch 2023-2 Differential Geometry (서동휘) file 수학연구소 서동휘
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Geometric Group Dynamics (서동균) file 수학연구소 서동균
수학강연회 Variational Methods without Nondegeneracy file POSTECH 변재형
수학강연회 학부생을 위한 강연: Introduction to partial differential equations file 서울대학교 변순식
수학강연회 Theory and applications of partial differential equations file 서울대 변순식
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Probability Theory (변성수) file KIAS 변성수
수학강연회 1 is big enough to understand 3 file 카이스트 백형렬
수학강연회 Essential dimension of simple algebras file KAIST 백상훈
수학강연회 <학부생을 위한 ɛ 강연> Introduction to the incompressible Navier-Stokes equations file UNIST 배한택
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