Integer points enumerator of hypergraphic polytopes
Apstrakt
For a hypergraphic polytope there is a weighted quasisymmetric
function which enumerates positive integer points in its normal fan
and determines its f −polynomial. This quasisymmetric function
invariant of hypergraphs extends the Stanley chromatic symmetric
function of simple graphs. We consider a certain combinatorial
Hopf algebra of hypergraphs and show that universal morphism to
quasisymmetric functions coincides with this enumerator function.
We calculate the f −polynomial of uniform hypergraphic polytopes.
Ključne reči:
quasisymmetric function / hypergraph / hypergraphic polytope / combinatorial Hopf algebraIzvor:
Publications de l'Institut Mathematique, 2021Izdavač:
- Mathematical Institute of the Serbian Academy of Sciences and Arts