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Explore the advanced mathematical theory of dendric sequences in this 59-minute lecture that delves into the combinatorial properties and structural characteristics of these specialized word sequences. Learn about dendric sequences as introduced by Berthé et al., which encompass codings of regular interval exchange transformations and strict episturmian (Arnoux-Rauzy) sequences, representing significant generalizations of classical Sturmian sequences. Discover how dendricity is defined through the analysis of finite factors and the restricted behavior of surrounding letters, leading to important combinatorial constraints including affine factor complexity. Examine the fundamental properties of dendric sequences with particular emphasis on their relationship to return words, gaining insight into this decade-old mathematical framework that bridges combinatorics on words with dynamical systems theory. Recorded during the "Combinatorics, Automata, and Number Theory (CANT)" thematic meeting at the Centre International de Rencontres Mathématiques in Marseille, France, this presentation provides essential theoretical foundations for understanding these sophisticated mathematical structures and their applications in modern combinatorial research.
