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...elements and Cambrian lattices have figured in the study of quiver representations and various topics. Details are far beyond the scope of this article, but we refer the reader to the research papers =-=[1, 2, 23, 24]-=- and to Thomas’ chapter [49] in this volume. 6.3. Combinatorial Hopf algebras. Besides the Cambrian construction, there is another profitable generalization of the Tamari lattices in a different direc...