# Realizing Geometrically s-Permutahedra via Flow Polytopes

Time: 14:00 -- Location: LRI, 445

summary: In 2020, Ceballos and Pons defined s-decreasing trees with s
being a weak composition. They described an order on these objects
called the s-weak order which gives them the order structure of a
lattice. They further conjectured that this structure could be realized
geometrically as the 1-skeleton of a polyhedral subdivision of a certain
polytope. In this talk I will present 2 such realizations with the help
of flow polytopes that come from directed graphs. The first uses
triangulations of said polytopes while the second consists of mixed
subdivisions of hypercubes.

This is joint work with Rafael S. González D’León, Alejandro H. Morales,
Eva Philippe, Yannic Vargas, and Martha Yip.