Integer points enumerator of hypergraphic polytopes
Abstract
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.
Keywords:
quasisymmetric function / hypergraph / hypergraphic polytope / combinatorial Hopf algebraSource:
2021Publisher:
- Publications de l'Institut Mathematique
Funding / projects:
Collections
Institution/Community
GraFarTY - JOUR AU - Pešović, Marko PY - 2021 UR - https://grafar.grf.bg.ac.rs/handle/123456789/2333 AB - 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. PB - Publications de l'Institut Mathematique T1 - Integer points enumerator of hypergraphic polytopes DO - https://doi.org/10.2298/PIM200205001P ER -
@article{ author = "Pešović, Marko", year = "2021", abstract = "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.", publisher = "Publications de l'Institut Mathematique", title = "Integer points enumerator of hypergraphic polytopes", doi = "https://doi.org/10.2298/PIM200205001P" }
Pešović, M.. (2021). Integer points enumerator of hypergraphic polytopes. Publications de l'Institut Mathematique.. https://doi.org/https://doi.org/10.2298/PIM200205001P
Pešović M. Integer points enumerator of hypergraphic polytopes. 2021;. doi:https://doi.org/10.2298/PIM200205001P .
Pešović, Marko, "Integer points enumerator of hypergraphic polytopes" (2021), https://doi.org/https://doi.org/10.2298/PIM200205001P . .