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  4. On Polytopes Arising in Cluster Algebras&Finite Frames
 
Zitierlink URN
https://nbn-resolving.de/urn:nbn:de:gbv:46-00105315-13

On Polytopes Arising in Cluster Algebras&Finite Frames

Veröffentlichungsdatum
2016-02-12
Autoren
Haga, Tim  
Betreuer
Feichtner, Eva-Maria  
Gutachter
Yu, Josephine  
Zusammenfassung
Polytopes appear in many contexts, two being cluster algebras and finite frames. At first we study graph theoretic properties of polytopes arising in the context of cluster algebras of finite type. We introduce the basic terms and constructions for cluster algebras of finite type, then we consider their exchange graphs and give a conjecture about the Hamiltonicity of the exchange graphs. Then we study polytopes, which arise in the construction of finite frames with given lengths of frame vectors and given spectrum of the frame operator. After an introduction to finite frames, we give a non-redundant description of those polytopes for equal norm tight frames in terms of equations and inequalities. From this, we derive the dimension and number of facets of the polytopes. In this process we combinatorially obtain two isomorphisms between polytopes associated to frames. Afterwards we discuss how these isomorphisms are described by reversing the order of frame vectors and taking Naimark complements.
Schlagwörter
Polytopes

; 

Cluster Algebras

; 

Hilbert Space Frames

; 

Convex Geometry

; 

Combinatorics
Institution
Universität Bremen  
Fachbereich
Fachbereich 03: Mathematik/Informatik (FB 03)  
Dokumenttyp
Dissertation
Zweitveröffentlichung
Nein
Sprache
Englisch
Dateien
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Vorschaubild
Name

00105315-1.pdf

Size

649.84 KB

Format

Adobe PDF

Checksum

(MD5):8b01216f67448ca9c6396a97aa0b7f0b

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