Permutrees

Talk by Prof. Dr. Vincent Pilaud

Speaker invited by: Prof. Dr. Valentin Féray

Date: 04.04.17  Time: 11.15 - 12.15  Room: Y27H46

Permutrees are oriented and labeled trees satisfying certain local conditions around each vertex. They gather under the same roof several combinatorial families, including permutations, binary trees, and binary sequences. The talk will present their combinatorial, geometric and algebraic structure. In particular, we will show:

• the permutree lattice, which generalizes the weak order on permutations, the Tamari lattice on binary trees, and the boolean lattice on binary sequences;
• the permutreehedron, which generalizes the permutahedron, the associahedron, and the cube;
• the permutree Hopf algebra, which generalizes the Malvenuto-Reutenauer Hopf algebra on permutations, the Loday-Ronco Hopf algebra on binary trees, and Solomon's descent Hopf algebra on binary sequences.