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The ubiquitous ProuhetThueMorse sequence
 Sequences and their applications, Proceedings of SETA’98
, 1999
"... We discuss a wellknown binary sequence called the ThueMorse sequence, or the ProuhetThueMorse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The ProuhetThueMorse sequence appears to be som ..."
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Cited by 59 (8 self)
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We discuss a wellknown binary sequence called the ThueMorse sequence, or the ProuhetThueMorse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The ProuhetThueMorse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences.
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 25 (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.
Periodicity and Repetition in Combinatorics on Words
, 2004
"... This thesis concerns combinatorics on words. I present many results in this area, united by the common themes of periodicity and repetition. Most of these results have already appeared in journal or conference articles. Chapter 2  Chapter 5 contain the most significant contribution of this thesis ..."
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This thesis concerns combinatorics on words. I present many results in this area, united by the common themes of periodicity and repetition. Most of these results have already appeared in journal or conference articles. Chapter 2  Chapter 5 contain the most significant contribution of this thesis in the area of combinatorics on words. Below we give a brief synopsis of each chapter. Chapter 1 introduces the subject area in general and some background information. Chapter 2 and Chapter 3 grew out of attempts to prove the Decreasing Length Conjecture (DLC). The DLC states that if # is a morphism over an alphabet of size n then for any word w, there exists 0 (w). The DLC was proved by S. Cautis and S. Yazdani in Periodicity, morphisms, and matrices in Theoret. Comput. Sci.
PERFECT MAGIC CUBES OF ORDER 4 m
"... It has long been known that there exists a perfect magic cube of order n where n £ 3, 59 75 2m, and km with m odd and m> _ 1. That they do not exist for orders 2, 3, and 4 is not difficult to show. Recently, several authors have constructed perfect magic cubes of order 7. We shall give a method f ..."
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It has long been known that there exists a perfect magic cube of order n where n £ 3, 59 75 2m, and km with m odd and m> _ 1. That they do not exist for orders 2, 3, and 4 is not difficult to show. Recently, several authors have constructed perfect magic cubes of order 7. We shall give a method for constructing perfect magic cubes of orders n km with m odd and m _> 7.