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Explore the mathematical theory of dendric sequences in this 54-minute lecture that introduces a decade-old concept developed by Berthé et al. Learn how dendric sequences encompass codings of regular interval exchange transformations and strict episturmian (or Arnoux-Rauzy) sequences, which represent significant generalizations of Sturmian sequences. Discover how dendricity is defined through the analysis of finite factors and the restricted behavior of surrounding letters, leading to combinatorial restrictions such as affine factor complexity. Survey the fundamental properties of dendric sequences with particular focus on their relationship to return words, gaining insight into this important area of combinatorial mathematics and sequence theory.
