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## Simplices of f-vectors

In this thesis the properties of the convex hulls of the sets of f-vectors of simplicial complexes on p vertices are investigated. The work is primarily constrained to the convex hulls of the sets of f-vectors of simplicial complexes of dimension at most 2 and 3. We study the functions which count the number of lattice points in these convex hulls and in their integral dilations. Also, the center of mass for these sets of f-vectors is studied. For the convex hulls of the sets of f-vectors with cardinality at most 3 we also investigate whether there is a compact rational function representing its f-vectors. Chapter 6 is devoted to researching whether there is any relationship between the number of f-vectors and the total number of lattice points in the convex hulls of the sets f-vectors with cardinality at most n.

Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-159826 |

Date | January 2019 |

Creators | Kupreyeva, Aliaksandra |

Publisher | Linköpings universitet, Matematiska institutionen |

Source Sets | DiVA Archive at Upsalla University |

Language | English |

Detected Language | English |

Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |

Format | application/pdf |

Rights | info:eu-repo/semantics/openAccess |

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