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Axel Thue's work on repetitions in words
 Invited Lecture at the 4th Conference on Formal Power Series and Algebraic Combinatorics
, 1992
"... The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched. ..."
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Cited by 22 (3 self)
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The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.
Extremal Infinite OverlapFree Binary Words
 Electronic J. Combinatorics
, 1997
"... Let t be the infinite fixed point, starting with 1, of the morphism :0#01, 1 # 10. An infinite word over {0, 1} is said to be overlapfree if it contains no factor of the form axaxa, where a #{0,1}and x #{0,1} # . We prove that the lexicographically least infinite overlapfree binary word begi ..."
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Cited by 8 (6 self)
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Let t be the infinite fixed point, starting with 1, of the morphism :0#01, 1 # 10. An infinite word over {0, 1} is said to be overlapfree if it contains no factor of the form axaxa, where a #{0,1}and x #{0,1} # . We prove that the lexicographically least infinite overlapfree binary word beginning with any specified prefix, if it exists, has a su#x which is a su#x of t. In particular, the lexicographically least infinite overlapfree binary word is 001001t. Keywords: Homomorphism, fixed point, overlapfree word. 1991 Mathematics Subject Classification: Primary 68R15. 1 the electronic journal of combinatorics 5 (1998),#R27 2 1 Introduction Since the pioneering work of Thue [14, 15] (see also [5]) the overlapfree words on a finite alphabet, i.e., those words that do not contain a factor axaxa,wherexis a word and a a letter, have been studied extensively. The question of extremality (for the lexicographic order) of overlapfree binary infinite words seems to have been addre...