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Face numbers of polytopes and complexes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7497-2764
2017 (English)In: Handbook of Discrete and Computational Geometry, Third Edition, CRC Press , 2017, p. 449-475Chapter in book (Other academic)
Abstract [en]

Geometric objects are often put together from simple pieces according to certain combinatorial rules. As such, they can be described as complexes with their constituent cells, which are usually polytopes and often simplices. Many constraints of a combinatorial and topological nature govern the incidence structure of cell complexes and are therefore relevant in the analysis of geometric objects. Since these incidence structures are in most cases too complicated to be well understood, it is worthwhile to focus on simpler invariants that still say something nontrivial about their combinatorial structure. The invariants to be discussed in this chapter are the f-vectors f = (f 0, f 1, …) $ f=(f_0, f_1, \dots) $, where f i $ f_i $ is the number of i-dimensional cells in the complex. 

Place, publisher, year, edition, pages
CRC Press , 2017. p. 449-475
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Mathematics
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URN: urn:nbn:se:kth:diva-236870DOI: 10.1201/9781315119601Scopus ID: 2-s2.0-85052675710ISBN: 9781498711425 (print)ISBN: 9781498711395 (print)OAI: oai:DiVA.org:kth-236870DiVA, id: diva2:1270873
Note

QC 20181214

Available from: 2018-12-14 Created: 2018-12-14 Last updated: 2018-12-14Bibliographically approved

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Björner, Anders.

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