Vortrag
Chromatic problems in polytope Hopf algebras
Vortrag von Dr. Raúl Queiroz do Vale de Noronha Pen (Penaguião)
Datum: 18.12.17 Zeit: 14.00 - 14.45 Raum: Y27H28
The chromatic symmetric function on graphs is a central chromatic invariant on graphs not only because of the information that it contains and the conjectures that arise but also because of its analogues in other combinatorial objects. We are going to talk about chromatic maps in other combinatorial spaces, in particular the generalised permutahedra. We will explore a little bit the kernel problem of these chromatic symmetric functions, i.e. trying to find generators of the kernel of this map.
The generalised permutahedra form a well behaved class of polytopes that contains the permutahedra, associahedra and graph zonotopes and it can be endowed with a Hopf algebra structure. It has been seen that many combinatorial objects like graphs and matroids can be embedded in this family preserving the Hopf algebra structure and the chromatic function. This tells us that the kernel problem in generalised permutahedra is of interest.
To tackle the kernel problem on graphs, the problem is solved with the help of some relations introduced earlier, but on the nestoehdra, a subclass of the generalised permutahedra, some elements on the kernel have to be presented first.