Results 1 
4 of
4
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. ..."
Abstract

Cited by 25 (3 self)
 Add to MetaCart
(Show Context)
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.
The origins of combinatorics on words
, 2007
"... We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. Other early results were obtained as a byproduct of investigations on various combinatorial objects. For example, paths in graphs are encoded by words in a natural way, and conversely, the Cayley graph of a group or a semigroup encodes words by paths. We give in this text an account of this twosided interaction.
Trees and Term Rewriting in 1910: On a Paper by Axel Thue
"... Many of Axel Thue's ideas have been influential in theoretical computer science. In particular, Thue systems, semiThue systems and his work on the combinatorics of words are wellknown. Here we consider his 1910 paper which contains many notions and ideas about trees, term rewriting and word p ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Many of Axel Thue's ideas have been influential in theoretical computer science. In particular, Thue systems, semiThue systems and his work on the combinatorics of words are wellknown. Here we consider his 1910 paper which contains many notions and ideas about trees, term rewriting and word problems which are surprisingly modern and have later come to play important roles in mathematics, logic, and computer science.
Formal Mathematical Systems including a Structural Induction Principle
, 2005
"... This study provides a general frame for the generation of languages in recursive systems closely related to formal grammars, for the predicate calculus and a constructive induction principle. We introduce recursive systems generating the recursively enumerable relations between lists of terms, the b ..."
Abstract
 Add to MetaCart
(Show Context)
This study provides a general frame for the generation of languages in recursive systems closely related to formal grammars, for the predicate calculus and a constructive induction principle. We introduce recursive systems generating the recursively enumerable relations between lists of terms, the basic objects under consideration. A recursive system consists of axioms which are special quantifierfree positive horn formulas and of special rules of inference. Its extension to formal mathematical systems includes the predicate calculus as well as a structural induction principle with respect to the axioms of the underlying recursive system. We have also formulated our main results about elementary proof theory for quite general restrictions in the argument lists of the formulas, which enables different kind of applications. 0