The Tamari lattice is a quotient of the weak order

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A relation between the anticyclic structure of the dendriform operad and the Coxeter transformations in the Grothendieck groups of the derived categories of modules over the

We define a subset of balanced trees where elements hold a peculiar position in the Tamari lattice and we give, using the synchronous grammar generating these, a functional equation

Hence, identifying in such trees the x with leaves, S bi only generates balanced binary trees such that each of its node r with −1 as imbalance value can be marked provided that

The sets of permutations corresponding to the linear extensions of the binary trees of size n form a partition of S n and more precisely, each set is an interval of the right weak

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