Abstract:
Permutrees are combinatorial objects that generalize and amalgam permutations, binary trees, binary words, and Cambrian trees. In this talk we will give a quick introduction to permutrees and introduce two generalizations of bracket vectors of binary trees. We will see how these generalizations encode algebraic and geometric properties of the rotation lattice on permutrees. In particular, how they lead to a meet operation in said lattice and the construction of a cubical complex for each permutreehedra.