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Integer points enumerator of hypergraphic polytopes

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2021
hypergraphsarxiv.pdf (256.5Kb)
Authors
Pešović, Marko
Article (Draft)
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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 algebra
Source:
2021
Publisher:
  • Publications de l'Institut Mathematique
Funding / projects:
  • Topology, geometry and global analysis on manifolds and discrete structures (RS-174034)

DOI: https://doi.org/10.2298/PIM200205001P

ISSN: 0350-1302

[ Google Scholar ]
URI
https://grafar.grf.bg.ac.rs/handle/123456789/2333
Collections
  • Катедра за математику, физику и нацртну геометрију
  • Radovi istraživača / Researcher's publications
Institution/Community
GraFar
TY  - 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 . .

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