This is the website of the Combinatorial Polytope Theory (COMPOTE) project jointly funded by AEI (Spain) & DFG (Germany).
Combinatorial Polytope Theory is the study of the two-way fruitful interactions between polytopes and combinatorics.
The first research line on Combinatorics of Polytopes studies combinatorial properties of general polytopes. We will study face numbers of important families of polytopes that are neither simple nor simplicial and thus fall outside the scope of the g-theorem. Moreover, we will explore novel polytope constructions inspired by the study of the behavior of linear programming, and the connection of max-slope polytopes with deformed permutahedra.
The second research line on Polytopes of Combinatorics concerns the study of families of polytopes arising from combinatorics and algebra, such as the classical permutahedra and associahedra. Motivated by different perspectives on the associahedron, we will follow three specific research directions: the (semi)lattice congruences of the weak order and its various generalizations, the recent poset associahedra and their interpretation as nested complexes of face lattices of polytopes, and the geometric properties of the deformation cones of permutahedra.
