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This lecture presents a construction of a bijection between a class of 3-dimensional permutations avoiding certain patterns and triangle bases, which are specific sets of integer points from tiling theory. The existence of this bijection was previously conjectured by Nicolas Bonichon and Pierre-Jean Morel. Explore the mathematical connections between pattern-avoiding permutations and geometric structures in this 22-minute French-language presentation recorded during the "ALEA Days" thematic meeting at the Centre International de Rencontres Mathématiques (CIRM) in Marseille, France on March 20, 2025. The video is available in CIRM's Audiovisual Mathematics Library with features including chapter markers, keywords, abstracts, bibliographies, and Mathematics Subject Classification for enhanced navigation and research.
